id
string | vector
sequence | title
string | abstract
string | authors
string | categories
string | month
string | year
int64 | url
string |
|---|---|---|---|---|---|---|---|---|
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] | Three Manifolds and Graph Invariants | We show how the Turaev--Viro invariant can be understood within the framework of Chern--Simons theory with gauge group SU(2). We also describe a new invariant for certain class of graphs by interpreting the triangulation of a manifold as a graph consisiting of crossings and vertices with three lines. We further show, for $S^3$ and $RP^3$, that the Turaev-Viro invariant is the square of the absolute value of their respective partition functions in SU(2) Chern--Simons theory and give a method of evaluating the later in a closed form for lens spaces $L_{p,1}$. | S. Kalyana Rama and Siddhartha Sen | hep-th math.QA | December | 1,991 | https://arxiv.org/abs/hep-th/9112071 |
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] | Partition Functions and Topology-Changing Amplitudes in the 3D Lattice Gravity of Ponzano and Regge | We define a physical Hilbert space for the three-dimensional lattice gravity of Ponzano and Regge and establish its isomorphism to the ones in the $ISO(3)$ Chern-Simons theory. It is shown that, for a handlebody of any genus, a Hartle-Hawking-type wave-function of the lattice gravity transforms into the corresponding state in the Chern-Simons theory under this isomorphism. Using the Heegaard splitting of a three-dimensional manifold, a partition function of each of these theories is expressed as an inner product of such wave-functions. Since the isomorphism preserves the inner products, the partition function of the two theories are the same for any closed orientable manifold. We also discuss on a class of topology-changing amplitudes in the lattice gravity and their relation to the ones in the Chern-Simons theory. | Hirosi Ooguri | hep-th | December | 1,991 | https://arxiv.org/abs/hep-th/9112072 |
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] | Higher-Rank Supersymmetry and Topological Field Theory | The $N=2$ minimal superconformal model can be twisted yielding an example of topological conformal field theory. In this article we investigate a Lie theoretic extension of this process. | Toshiya Kawai, Taku Uchino and Sun-Kil Yang | hep-th | December | 1,991 | https://arxiv.org/abs/hep-th/9112073 |
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] | Non-linear WKB Analysis of the String Equation | We apply non-linear WKB analysis to the study of the string equation. Even though the solutions obtained with this method are not exact, they approximate extremely well the true solutions, as we explicitly show using numerical simulations. ``Physical'' solutions are seen to be separatrices corresponding to degenerate Riemann surfaces. We obtain an analytic approximation in excellent agreement with the numerical solution found by Parisi et al. for the $k=3$ case. | F. Fucito, A. Gamba, M. Martellini and O. Ragnisco | hep-th | December | 1,991 | https://arxiv.org/abs/hep-th/9112074 |
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] | Exactly Solvable Potentials and Quantum Algebras | A set of exactly solvable one-dimensional quantum mechanical potentials is described. It is defined by a finite-difference-differential equation generating in the limiting cases the Rosen-Morse, harmonic, and P\"oschl-Teller potentials. General solution includes Shabat's infinite number soliton system and leads to raising and lowering operators satisfying $q$-deformed harmonic oscillator algebra. In the latter case energy spectrum is purely exponential and physical states form a reducible representation of the quantum conformal algebra $su_q(1,1)$. | V.Spiridonov | hep-th | December | 1,991 | https://arxiv.org/abs/hep-th/9112075 |
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] | Lectures on W algebras and W gravity | We give a review of the extended conformal algebras, known as $W$ algebras, which contain currents of spins higher than 2 in addition to the energy-momentum tensor. These include the non-linear $W_N$ algebras; the linear $W_\infty$ and $W_{1+\infty}$ algebras; and their super-extensions. We discuss their applications to the construction of $W$-gravity and $W$-string theories. | C.N. Pope | hep-th | December | 1,991 | https://arxiv.org/abs/hep-th/9112076 |
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] | Rational Curves on Calabi-Yau Threefolds | The point is to compare the mathematical meaning of the ``number of rational curves on a Calabi-Yau threefold'' to the meaning ascribed to the same notion by string theorists. | Sheldon Katz | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202001 |
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] | Gorenstein Threefold Singularities with Small Resolutions via Invariant Theory for Weyl Groups | We classify simple flops on smooth threefolds, or equivalently, Gorenstein threefold singularities with irreducible small resolution. There are only six families of such singularities, distinguished by Koll{\'a}r's {\em length} invariant. The method is to apply invariant theory to Pinkham's construction of small resolutions. As a by-product, generators of the ring of invariants are given for the standard action of the Weyl group of each of the irreducible root systems. | Sheldon Katz and David R. Morrison | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202002 |
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] | Complex Contact Threefolds and Their Contact Curves | A complex contact threefold is a threefold with a two-dimensional non-integrable holomorphic distribution. A contact curve on a contact threefold is an integrable curve of the distribution. This work was inspired by two papers of Bryant, in which he used complex contact geometry to study superminimal surfaces in four-sphere and to investigate exotic holonomies. The present paper is devoted to systematical studies of contact threefold and contact curves on them. We generalize a result of Bryant and answer a question of his. | Yun-Gang Ye | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202003 |
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] | Mirror symmetry and rational curves on quintic threefolds: a guide for mathematicians | We give a mathematical account of a recent string theory calculation which predicts the number of rational curves on the generic quintic threefold. Our account involves the interpretation of Yukawa couplings in terms of variations of Hodge structure, a new $q$-expansion principle for functions on the moduli space of Calabi-Yau manifolds, and the ``mirror symmetry'' phenomenon recently observed by string theorists. | David R. Morrison | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202004 |
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] | On the difference between real and complex arrangements | Let $B$ be an arrangement of linear complex hyperplanes in $C^d$. Then a classical result by Orlik \& Solomon asserts that the cohomology algebra of the complement can be constructed from the combinatorial data that are given by the intersection lattice. If $B'$ is, more generally, a $2$-arrangement in $R^{2d}$ (an arrangement of real subspaces of codimension $2$ with even-dimensional intersections), then the intersection lattice still determines the cohomology {\it groups} of the complement, as was shown by Goresky \& MacPherson. We prove, however, that for $2$-arrangements the cohomology {\it algebra} is not determined by the intersection lattice. It encodes extra information on sign patterns, which can be computed from determinants of linear relations or, equivalently, from linking coefficients in the sense of knot theory. This also allows us (in the case $d=2$) to identify arrangements with the same lattice but different fundamental groups. | G\"unter M. Ziegler | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202005 |
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] | Twistors, Kaehler Manifolds, and Bimeromorphic Geometry II | Using examples of compact complex 3-manifolds which arise as twistor spaces, we show that the class of compact complex manifolds bimeromorphic to K\"ahler manifolds is not stable under small deformations of complex structure. | Claude LeBrun and Yat-Sun Poon | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202006 |
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] | The algebraic de Rham theorem for toric varieties | On an arbitrary toric variety, we introduce the logarithmic double complex, which is essentially the same as the algebraic de Rham complex in the nonsingular case, but which behaves much better in the singular case. Over the field of complex numbers, we prove the toric analog of the algebraic de Rham theorem which Grothendieck formulated and proved for general nonsingular algebraic varieties re-interpreting an earlier work of Hodge-Atiyah. Namely, for a finite simplicial fan which need not be complete, the complex cohomology groups of the corresponding toric variety as an analytic space coincide with the hypercohomology groups of the single complex associated to the logarithmic double complex. They can then be described combinatorially as Ishida's cohomology groups for the fan. We also prove vanishing theorems for Ishida's cohomology groups. As a consequence, we deduce directly that the complex cohomology groups vanish in odd degrees for toric varieties which correspond to finite simplicial fans with full-dimensional convex support. In the particular case of complete simplicial fans, we thus have a direct proof for an earlier result of Danilov and the author. | Tadao Oda | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202007 |
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] | On irregular links at infinity of algebraic plane curves | We give two proofs of a conjecture of the first author (Inv. Math. 98, 1989) that a reduced algebraic plane curve is regular at infinity if and only if its link at infinity is a regular toral link. This conjecture has also been proved by Ha H.~V. using Lojasiewicz numbers at infinity. Our first proof uses the polar invariant and the second proof uses linear systems of plane curve singularities. The second approach (based on a paper in preparation) also proves a stronger conjecture (loc. cit.) describing topologically the regular link at infinity associated with an irregular link at infinity. | Walter D. Neumann and Le Van Thanh | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202008 |
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] | On a Grauert-Riemenschneider vanishing theorem for Frobenius split varieties in characteristic p | This paper is about sheaf cohomology for varieties (schemes) in characteristic $p>0$. We assume the presence of a Frobenius splitting. (See V.B. Mehta and A. Ramanathan, Frobenius splitting and cohomology vanishing for Schubert varieties, Annals of Math. 122 (1985), 27--40). The main result is that a non-zero higher direct image under a proper map of the ideal sheaf of a compatibly Frobenius split subvariety can not have a support whose inverse image is contained in that subvariety. Earlier vanishing theorems for Frobenius split varieties were based on direct limits and Serre's vanishing theorem, but our theorem is based on inverse limits and Grothendieck's theorem on formal functions. The result implies a Grauert--Riemenschneider type theorem. | V. B. Mehta and Wilberd van der Kallen | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202009 |
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] | Another Relation Between Approaches to the Schottky Problem | The recent extensive work on different approaches to the Schottky problem has produced marked progress on several fronts. At the same time, it has become apparent that there exist very close connections between the various characterizations of Jacobian varieties described in Mumford's classic lectures {\it Curves and Their Jacobians\/}. Until now, the approach via double translation manifolds has seemed to be quite different from other approaches to the Schottky problem. The purpose of this paper is to bring this last approach ``into the fold'' as it were, and to show precisely how it relates to characterizations of Jacobians based on trisecants and flexes of the Kummer variety, and the K.P. equation. | John B. Little | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202010 |
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] | The Geometry and Arithmetic of Elliptic Surfaces | We survey some aspects of the theory of elliptic surfaces and give some results aimed at determining the Picard number of such a surface. For the surfaces considered, this will be equivalent to determining the Mordell-Weil rank of an elliptic curve defined over a function field in one variable. An interesting conjecture concerning Galois actions on the relative de~Rham cohomology of these surfaces is discussed. | Peter F. Stiller | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202011 |
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] | Cohomology of coherent sheaves on a proper scheme | (Makes a Gamma-acylic coherent resolution of a coherent sheaf on a projection scheme.) | George R. Kempf | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202012 |
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] | Deformations of Semi-Euler Characteristics | (Generalizes theorem of Atiyah and Mumford.) | George R. Kempf | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202013 |
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] | Degenerations of generalized KNN algebras on tori | Degenerations of Lie algebras of meromorphic vector fields on elliptic curves (i.e. complex tori) which are holomorphic outside a certain set of points (markings) are studied. By an algebraic geometric degeneration process certain subalgebras of Lie algebras of meromorphic vector fields on P^1 the Riemann sphere are obtained. In case of some natural choices of the markings these subalgebras are explicitly determined. It is shown that the number of markings can change. AMS subject classification (1991): 17B66, 17B90, 14F10, 14H52, 30F30, 81T40 | Martin Schlichenmaier | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202014 |
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] | Note on curves in a Jacobian | For a curve C, viewed as a cycle in its Jacobian, we study its image n_*C under multiplication by n on JC. We prove that the subgroup generated by these cycles, in the Chow group modulo algebraic equivalence, has rank at most d-1, where d is the gonality of C. We also discuss some general facts on the action of n_* on the Chow groups. | Elisabetta Colombo and Bert van Geemen | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202015 |
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] | Congruences for real algebraic curves on an ellipsoid | The problem of arrangement of a real algebraic curve on a real algebraic surface is related to the 16th Hilbert problem. We prove in this paper new restrictions on arrangement of nonsingular real algebraic curves on an ellipsoid. These restrictions are analogues of Gudkov-Rokhlin, Gudkov-Krakhnov-Kharlamov, Kharlamov-Marin congruences for plane curves (see e.g. \cite{V} or \cite{V1}). To prove our results we follow Marin approach \cite{Marin} that is a study of the quotient space of a surface under the complex conjugation. Note that the Rokhlin approach \cite{R} that is a study of the 2-sheeted covering of the surface branched along the curve can not be directly applied for a proof of Theorem \ref{Rokhlin} since the homology class of a curve of Theorem \ref{Rokhlin} can not be divided by 2 hence such a covering space does not exist. | G.Mikhalkin | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202016 |
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] | Extensions of Rokhlin congruence for curves on surfaces | The subject of this paper is the problem of arrangement of a real nonsingular algebraic curve on a real non-singular algebraic surface. This paper contains new restrictions on this arrangement extending Rokhlin and Kharlamov-Gudkov-Krakhnov congruences for curves on surfaces. | G.Mikhalkin | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202017 |
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] | Arithmetically Cohen-Macaulay Curves cut out by Quadrics | Addressing a question of M. Stillman, it had been shown by Ein, Eisenbud, and the author that in a projective space of dimension at most 5, every arithmetically Cohen-Macaulay curve which is cut out by quadrics scheme- theoretically also has its homogeneous ideal generated by quadrics. In this note it is shown that this is not the case in higher dimensional spaces. | Sheldon Katz | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202018 |
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] | The cohomological Brauer group of a toric variety | Toric varieties are a special class of rational varieties defined by equations of the form {\it monomial = monomial}. For a good brief survey of the history and role of toric varieties see [10]. Any toric variety $X$ contains a cover by affine open sets described in terms of arrangements (called fans) of convex bodies in $\Bbb R^r$. The coordinate rings of each of these affine open sets is a graded ring generated over the ground field by monomials. As a consequence, toric varieties provide a good context in which cohomology can be calculated. The purpose of this article is to describe the second \'etale cohomology group with coefficients in the sheaf of units of any toric variety $X$. This is the so-called cohomological Brauer group of $X$. | Frank DeMeyer, Tim Ford, and Rick Miranda | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202019 |
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] | Disproving Hibi's Conjecture with CoCoA or Projective Curves with bad Hilbert Functions | In this paper we show how to combine different techniques from Commutative Algebra and a systematic use of a Computer Algebra System (in our case mainly CoCoA) in order to explicitly construct Cohen-Macaulay domains, which are standard $k$-algebras and whose Hilbert function is ``bad". In particular we disprove a well-known conjecture by Hibi. | G. Niesi, L. Robbiano | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202020 |
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] | Grobner bases and extension of scalars | This paper studies the behavior of Grobner bases with respect to extensions of scalars. We prove that an extension of scalars commutes with taking Grobner bases iff the extension is flat. We consider what information can be deduced about fibers of a family, from the Grobner basis of the defining ideal of the family itself. This information can be used to construct algorithms, such as to find locii over which a map is finite, or an isomorphism. | Dave Bayer, Andre Galligo, Mike Stillman | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202021 |
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] | Classical Polylogarithms | This paper is an introduction to classical polylogarithms and is an expanded version of a talk given by the author at the Motives conference. Topics covered include, monodromy; the polylogarithm local systems; Bloch's constructions of regulators using the dilogarithm; polylog locals systems as variations of mixed Hodge structre; the polylogarithm quotient of the fundamental group of C - {0,}. It is intended as background for understanding recent work of Beilinson, Deligne, and Goncharov. | Richard Hain | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202022 |
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] | Regulators and characteristic classes of flat bundles | This is a substantial revision of the older version of this paper. The main result of the old version (the equality, up to a factor of 2 of the Beilinson and Borel regulators) is now a conjecture. The main results give equality of Beilinson chern classes and Cheeger-Simons-Chern classes in various situations such as for flat bundles over quasi projective varieties. We also prove the equality (up to a factor of two) of the Borel regulator element and the universal Cheeger-Simons Chern class. | Johan Dupont, Richard Hain and Steven Zucker | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202023 |
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] | Sur la cohomologie de certains espaces de modules de fibr\'es vectoriels | Let M be a moduli space of stable vector bundles on a curve with rank and degree fixed and coprime. We give a simple proof that the rational cohomology of M is generated by the Kunneth components of the Chern classes of the universal bundle. The proof applies also to some moduli spaces of vector bundles over higher-dimensional varieties. | A. Beauville | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202024 |
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] | The Singularities of the parameter surface of a minimal elliptic threefold | Let f : X -> S be any elliptic fibration. If X has dimension 3 and is not uniruled, then X has a minimal model (with terminal singularities) [Mori]. In earlier work we have shown that there exists a birationally equivalent elliptic fibration p: Y -> T such that Y is minimal and a multiple of K_Y can be expressed as the pullback of a divisor from T. Moreover T has at worst quotient singularities; it is not difficult to find examples where T is actually singular. In this paper we describe the singularities of this parameter surface T in the case of no multiple fibers. Although T is not uniquely determined by the birational equivalence class of the fibration, any two such T are related by a particular kind of birational map. | A. Grassi | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202025 |
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] | Picard-Fuchs equations and mirror maps for hypersurfaces | We describe a strategy for computing Yukawa couplings and the mirror map, based on the Picard-Fuchs equation. (Our strategy is a variant of the method used by Candelas, de la Ossa, Green, and Parkes in the case of quintic hypersurfaces.) We then explain a technique of Griffiths which can be used to compute the Picard-Fuchs equations of hypersurfaces. Finally, we carry out the computation for four specific examples (including quintic hypersurfaces, previously done by Candelas et al.). This yields predictions for the number of rational curves of various degrees on certain hypersurfaces in weighted projective spaces. Some of these predictions have been confirmed by classical techniques in algebraic geometry. | David R. Morrison | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202026 |
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] | Cohomological and Cycle-theoretic connectivity | One of the themes in algebraic geometry is the study of the relation between the ``topology'' of a smooth projective variety and a (``general'') hyperplane section. Recent results of Nori produce cohomological evidence for a conjecture that a general hypersurface of sufficently large degree should have no ``interesting'' cycles. We compute precise bounds for these results and show by example that there are indeed interesting cycles for degrees that are not high enough. In a different direction Esnault, Nori and Srinivas have shown connectivity for intersections of small multidegree. We show analogous cycle-theoretic connectivity results. | Kapil H. Paranjape | alg-geom math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202027 |
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] | Complex Divisors on Algebraic Curves and Some Applications to String Theory | These are notes of a talk to the International Conference on Algebra in honor of A. I. Mal'tsev, Novosibirsk, USSR, 1989 (to appear in Contemporary Mathematics). The concept of a divisor with complex coefficients on an algebraic curve is introduced. We consider families of complex divisors, or, equivalently, families of invertible sheaves and define Arakelov-type metrics on some invertible sheaves produced from them on the base. We apply this technique to obtain a formula for the measure on the moduli space that gives tachyon correlators in string theory. | A. A. Voronov | alg-geom hep-th math.AG | February | 1,992 | https://arxiv.org/abs/alg-geom/9202028 |
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] | Exceptional linear systems on curves on Enriques surfaces | The main purpose in this paper is to study the gonality, the Clifford index and the Clifford dimension on linearly equivalent smooth curves on Enriques surfaces. The method is similar to techniques of M.Green $\&$ R.Lazarsfeld and G.Pareschi. | Severinas Zube | alg-geom math.AG | March | 1,992 | https://arxiv.org/abs/alg-geom/9203001 |
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] | Prym Varieties and Integrable Systems | A new relation between Prym varieties of arbitrary morphisms of algebraic curves and integrable systems is discovered. The action of maximal commutative subalgebras of the formal loop algebra of GL(n) defined on certain infinite-dimensional Grassmannians is studied. It is proved that every finite-dimensional orbit of the action of traceless elements of these commutative Lie algebras is isomorphic to the Prym variety associated with a morphism of algebraic curves. Conversely, it is shown that every Prym variety can be realized as a finite-dimensional orbit of the action of traceless diagonal elements of the formal loop algebra, which defines the multicomponent KP system. | Yingchen Li and Motohico Mulase | alg-geom math.AG | March | 1,992 | https://arxiv.org/abs/alg-geom/9203002 |
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] | Computing the Cohomological Brauer Group of a Toric Variety | The purpose of this article is to show how one might compute the \'etale cohomology groups $H^p_{\acute{e}t}(X,G_m)$ in degrees $p=0$, $1$ and $2$ of a toric variety $X$ with coefficients in the sheaf of units. The method is to reduce the computation down to the problem of diagonalizing a matrix with integral coefficients. The procedure outlined in this article has been fully implemented by the author as a program written in the ``C'' programming language. | Timothy J. Ford | alg-geom math.AG | March | 1,992 | https://arxiv.org/abs/alg-geom/9203003 |
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] | On the Abel-Jacobi Map for Divisors of Higher Rank on a Curve | The aim of this paper is to present an algebro-geometric approach to the study of the geometry of the moduli space of stable bundles on a smooth projective curve defined over an algebraically closed field $k$, of arbitrary characteristic. This establishes a bridge between the arithmetic approach of Harder, Narasimhan et al. and the gauge group approach of Atiyah and Bott. One of the basic ideas is to consider a notion of divisor of higher rank and a suitable Abel-Jacobi map generalizing the classical notions in rank one. | Emili Bifet, Franco Ghione and Maurizio Letizia | alg-geom math.AG | March | 1,992 | https://arxiv.org/abs/alg-geom/9203004 |
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] | Homotopy groups of the complements to singular hypersurfaces,II | The homotopy group $\pi_{n-k} ({\bf C}^{n+1}-V)$ where $V$ is a hypersurface with a singular locus of dimension $k$ and good behavior at infinity is described using generic pencils. This is analogous to the van Kampen procedure for finding a fundamental group of a plane curve. In addition we use a certain representation generalizing the Burau representation of the braid group. A divisibility theorem is proven that shows the dependence of this homotopy group on the local type of singularities and behavior at infinity. Examples are given showing that this group depends on certain global data in addition to local data on singularities. | A.Libgober | alg-geom math.AG | March | 1,992 | https://arxiv.org/abs/alg-geom/9203005 |
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] | Weierstrass Gap Sequence at Total Inflection Points of Nodal Plane Curves | Let $\Gamma$ be a plane curve of degree $d$ with $\delta$ ordinary nodes and no other singularities. If $P$ is a smooth point on $\Gamma$ then the Weierstrass gap sequence at $P$ is considered as that at the corresponding point on the normalization of $\Gamma$. A smooth point $P\in\Gamma$ is called a total inflection point if $i(\Gamma ,T;P)=d$ where $T$ is the tangent line to $\Gamma$ at $P$. There are many possible Weierstrass gap sequences at total inflection points. Our main results are: Among them (1) There exists a pair $(P,\Gamma )$ such that the gap sequence at $P$ is the minimal (in the sense of weight). (2) There exists a pair $(P,\Gamma )$ such that the gap sequence at $P$ is the maximal (resp. up to 1 maximal). And we characterize these cases in the sense of location of nodes. | Marc Coppens and Takao Kato | alg-geom math.AG | April | 1,992 | https://arxiv.org/abs/alg-geom/9204001 |
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] | Report on the Torsion of the Differential Module of an algebraic Curve | There is a conjecture, that the torsionfreeness of the module of differentials in a point of an algebraic or algebroid curve should imply that the curve is non singular at that point. A report on the main results is given. | Robert W. Berger | alg-geom math.AC math.AG | May | 1,992 | https://arxiv.org/abs/alg-geom/9205001 |
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] | Cohomology, Symmetry, and Perfection | One of the aims of this paper is to better explain the philosophy behind the computations in [E.Bifet, C.De Concini,C.Procesi Cohomology of Regular Embeddings ] and to place them in a wider conceptual setting. Another aim of the paper is to outline in the last section an ``equivariant'' approach to some key results in the theory of toric varieties. The text of the first three sections follows closely a talk delivered at the University of Copenhagen in July 1989 on the occasion of the Zeuthen Symposium. This paper is dedicated to the memory of my friend Pere Menal and will appear in the Fall 1992 issue, dedicated to his memory, of Publicacions Matem\`atiques, Universitat Aut\`onoma de Barcelona. | Emili Bifet | alg-geom math.AG | May | 1,992 | https://arxiv.org/abs/alg-geom/9205002 |
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] | Chern classes and degenerations of hypersurfaces and their lines | We study limiting lines on degenerations of generic hypersurfaces in $P^n$. | Xian Wu | alg-geom math.AG | May | 1,992 | https://arxiv.org/abs/alg-geom/9205003 |
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] | Notes on Kodaira energies of polarized varieties | The Kodaira energy of a polarized manifold (M,L) is defined by \kappa\epsilon(M,L)=-Inf{t\in Q|\kappa(K+tL)\ge 0}. Here we propose a couple of conjectures and announce several partial results. 3-dimensional cases are mainly considered. A hard copy is available on request to the author. | Takao Fujita | alg-geom math.AG | May | 1,992 | https://arxiv.org/abs/alg-geom/9205004 |
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] | Linear orbits of d-tuples of points in P^1 | The group PGL(2) of linear transformations of the projective line acts naturally on the d-dimensional projective space P^d parametrizing configurations (`d-tuples') of points on the line. In this note we are concerned with the orbits of this action of PGL(2) on P^d. The closure of each orbit is a projective subvariety of P^d of which we determine the degree, the `boundary'--i.e., the complement of an orbit in its closure--, and the multiplicity at points of the boundary. These results are used to provide a complete classification of the non-singular orbit closures, and criteria for an orbit closure to be non-singular in codimension 1. | Paolo Aluffi, Carel Faber | alg-geom math.AG | May | 1,992 | https://arxiv.org/abs/alg-geom/9205005 |
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] | Upper Bounds for the Betti Numbers of a given Hilbert Function | From a Macaulay's paper it follows that a lex-segment ideal has the greatest number of generators (the 0-th Betti number $\b_0$) among all the homogeneous ideals with the same Hilbert function. In this paper we prove that this fact extends to every Betti number, in the sense that all the Betti numbers of a minimal free resolution of a lex segment ideal are bigger than or equal to the ones of any homogeneous ideal with the same Hilbert function. | Anna Maria Bigatti | alg-geom math.AG | May | 1,992 | https://arxiv.org/abs/alg-geom/9205006 |
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] | On the Tangent Space to the Universal Teichmuller Space | We find a remarkably simple relationship between the following two models of the tangent space to the Universal Teichm\"uller Space: (1) The real-analytic model consisting of Zygmund class vector fields on the unit circle; (2) The complex-analytic model comprising 1-parameter families of schlicht functions on the exterior of the unit disc which allow quasiconformal extension. Indeed, the Fourier coefficients of the vector field in (1) turn out to be essentially the same as (the first variations of) the corresponding power series coefficients in (2). These identities have many applications; in particular, to conformal welding, to the almost complex structure of Teichm\"uller space, to study of the Weil-Petersson metric, to variational formulas for period matrices, etc. These utilities are explored. | Subhashis Nag | alg-geom math.AG | May | 1,992 | https://arxiv.org/abs/alg-geom/9205007 |
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] | Linear orbits of smooth plane curves | The group PGL(3) of linear transformations of the projective plane acts naturally on the projective space parametrizing curves of a given degree. In this note we begin the study of the orbits of smooth curves under this action: we construct a resolution of the closure of the orbit of a given curve, and we use it to compute its degree. This turns out to depend only on the degree of the curve, the order of its automorphism group, and on the number and type of its flexes. This paper will appear on the Journal of Algebraic Geometry. | Paolo Aluffi, Carel Faber | alg-geom math.AG | June | 1,992 | https://arxiv.org/abs/alg-geom/9206001 |
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] | String Branchings on Complex Tori and Algebraic Representations of Generalized Krichever-Novikov Algebras | The propagation differential for bosonic strings on a complex torus with three symmetric punctures is investigated. We study deformation aspects between two point and three point differentials as well as the behaviour of the corresponding Krichever-Novikov algebras. The structure constants are calculated and from this we derive a central extension of the Krichever-Novikov algebras by means of b-c systems. The defining cocycle for this central extension deforms to the well known Virasoro cocycle for certain kinds of degenerations of the torus. AMS subject classification (1991): 17B66, 17B90, 14H52, 30F30, 81T40 | Andreas Ruffing, Thomas Deck, Martin Schlichenmaier | alg-geom math.AG | June | 1,992 | https://arxiv.org/abs/alg-geom/9206002 |
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] | Affine like Surfaces | We classify smooth surfaces whose higher cohomologies of i-forms for all i vanish. We show that if such a surface is not affine, then it has essentially two possibilities. | N. Mohan Kumar | alg-geom math.AG | June | 1,992 | https://arxiv.org/abs/alg-geom/9206003 |
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] | Extremal Rays and Null Geodesics on a Complex Conformal Manifold | This is a revised version of the paper submitted before. | Yun-Gang Ye | alg-geom math.AG | June | 1,992 | https://arxiv.org/abs/alg-geom/9206004 |
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] | Two Two-dimensional Terminations | Varieties with log terminal and log canonical singularities are considered in the Minimal Model Program, see \cite{...} for introduction. In \cite{shokurov:hyp} it was conjectured that many of the interesting sets, associated with these varieties have something in common: they satisfy the ascending chain condition, which means that every increasing chain of elements terminates. Philosophically, this is the reason why two main hypotheses in the Minimal Model Program: existence and termination of flips should be true and are possible to prove. In this paper we prove that the following two sets satisfy the ascending chain condition: 1. The set of minimal log discrepancies for $K_X+B$ where $X$ is a surface with log canonical singularities. 2. The set of groups $(b_1,...b_s)$ such that there is a surface $X$ with log canonical and numerically trivial $K_X+\sum b_jB_j$. The order on such groups is defined in a natural way. | Valery Alexeev | alg-geom math.AG | June | 1,992 | https://arxiv.org/abs/alg-geom/9206005 |
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] | Corps quadratiques dont le 5-rang du groupe des classes est >=3 | We prove the existence of infinitely many real and imaginary fields whose 5-rank of the class group is >=3. | Jean-Francois Mestre | alg-geom math.AG | June | 1,992 | https://arxiv.org/abs/alg-geom/9206006 |
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] | Rang de courbes elliptiques d'invariant donne | We prove that there exist infinitely many elliptic curves over \Q with given modular invariant, and rank >=2. Furthermore, there exist infinitely many elliptic curves over $\Q$ with invariant equal at 0 (resp. 1728) and rank >=6 (resp. >=4). | Jean-Francois Mestre | alg-geom math.AG | June | 1,992 | https://arxiv.org/abs/alg-geom/9206007 |
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] | The fibers of the Prym map | In this work we use the bigonal, trigonal and tetragonal constructions to describe the fibers of the Prym map P : R_{g} ---->A_{g-1} inthe cases when it is dominant, i.e. for g < 7. The most interesting cases are g = 5, where the fiber is a double cover of the Fano surface of lines on a cubic threefold, and g=6, where the map is generically finite (of degree 27) with Galois group WE_{6}, so that the general fiber has the structure of the 27 lines on a cubic surface. For g > 6, the map is known to be generically injective. The tetragonal construction gives many counterexamples to injectivity, and we conjecture that all noninjectivity is due to the tetragonal construction. | Ron Donagi | alg-geom math.AG | June | 1,992 | https://arxiv.org/abs/alg-geom/9206008 |
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] | The complex separation and extensions of Rokhlin congruence for curves on surfaces | The subject of this paper is the problem of arrangement of real algebraic curves on real algebraic surfaces. In this paper we extend Rokhlin, Kharlamov-Gudkov-Krakhnov and Kharlamov-Marin congruences for curves on surfaces and give some applications of this extension. For some pairs consisting of a surface and a curve on this surface (in particular for M-pairs) we introduce a new structure --- the complex separation that is separation of the complement of curve into two surfaces. In accordance with Rokhlin terminology the complex separation is a complex topological characteristic of real algebraic varieties. The complex separation is similar to complex orientations introduced by O.Ya.Viro (to the absolute complex orientation in the case when a curve is empty and to the relative complex orientation otherwise). In some cases we calculate the complex separation of a surface (for example in the case when surface is the double branched covering of another surface along a curve). With the help of these calculations applications of the extension of Rokhlin congruence gives some new restrictions for complex orientations of curves on a hyperboloid. | G.Mikhalkin | alg-geom math.AG | June | 1,992 | https://arxiv.org/abs/alg-geom/9206009 |
alg-geom/9207001 | [
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] | Completions of mapping class groups and the cycle $C - C^-$ | In this paper we study the proalgebraic completion of mapping class relative to their maps to the symplectic group. The main result is that the natural map from the unipotent (a.k.a. Malcev) completion of the Torelli group to the prounipotent radical of the Sp_g completion of the mapping class group is a non trivial central extension with kernel isomorphic to Q, at least when g \ge 8. The theorem is proved by relating the central extension to the line bundle associated to the archemidean height of the cycle C - C- in the Jacobian of the curve C. We also develop some of the basic theory of relative completions. | Richard Hain (Duke Univeristy) | alg-geom math.AG | July | 1,992 | https://arxiv.org/abs/alg-geom/9207001 |
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] | Open String Diagrams I: Topological Type | An arbitrary Feynman graph for string field theory interactions is analysed and the homeomorphism type of the corresponding world sheet surface is completely determined even in the non-orientable cases. Algorithms are found to mechanically compute the topological characteristics of the resulting surface from the structure of the signed oriented graph. Whitney's permutation-theoretic coding of graphs is utilized. | Subhashis Nag and Parameswaran Sankaran (The Institute of Mathematical Sciences C.I.T.Campus Madras) | alg-geom hep-th math.AG | August | 1,992 | https://arxiv.org/abs/alg-geom/9208001 |
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] | Abelian varieties over Q and modular forms | This paper gives a conjectural characterization of those elliptic curves over the field of complex numbers which "should" be covered by standard modular curves. The elliptic curves in question all have algebraic j-invariant, so they can be viewed as curves over Q-bar, the field of algebraic numbers. The condition that they satisfy is that they must be isogenous to all their Galois conjugates. Borrowing a term from B.H. Gross, "Arithmetic on elliptic curves with complex multiplication," we say that the elliptic curves in question are "Q-curves." Since all complex multiplication elliptic curves are Q-curves (with this definition), and since they are all uniformized by modular forms (Shimura), we consider only non-CM curves for the remainder of this abstract. We prove: 1. Let C be an elliptic curve over Q-bar. Then C is a Q-curve if and only if C is a Q-bar simple factor of an abelian variety A over Q whose algebra of Q-endomorphisms is a number field of degree dim(A). (We say that abelian varieties A/Q with this property are of "GL(2) type.") 2. Suppose that Serre's conjecture on mod p modular forms are correct (Ref: Duke Journal, 1987). Then an abelian variety A over Q is of GL(2)-type if and only if it is a simple factor (over Q) of the Jacobian J_1(N) for some integer N\ge1. (The abelian variety J_1(N) is the Jacobian of the standard modular | Kenneth A. Ribet | alg-geom math.AG | August | 1,992 | https://arxiv.org/abs/alg-geom/9208002 |
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] | Weierstrass weight of Gorenstein singularities with one or two branches | Let $X$ denote an integral, projective Gorenstein curve over an algebraically closed field $k$. In the case when $k$ is of characteristic zero, C. Widland and the second author have defined Weierstrass points of a line bundle on $X$. In the first section, this definition is extended to linear systems in arbitrary characteristic. This definition may be viewed as a generalization of the definitions of Laksov and St\"ohr-Voloch to the Gorenstein case. In the second section, an example is given to illustrate the definition. This example is a plane curve of arithmetic genus 3 in characteristic 2 such that the gap sequence at every smooth point (with respect to the dualizing bundle) is 1,2,5 and there are no smooth Weierstrass points. In the third section, the Weierstrass weight of a unibranch singularity (on a not necessarily rational curve) is computed in terms of its semigroup of values. In the final section, the Weierstrass weight of a singularity with precisely two branches (again assuming that the characteristic is zero) is computed. AMS Classification: Primary 14H55, Secondary 14H20. | A. Garcia and R.F. Lax | alg-geom math.AG | August | 1,992 | https://arxiv.org/abs/alg-geom/9208003 |
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0.13046307861804962,
0.12609922885894775,
-0.43566280603408813
] | Torsion Sections of Semistable Elliptic Surfaces | Let S be a torsion section of an elliptic surface with only I_n fibers. This article addresses the question: which components of singular fibers can S pass through? We give necessary criteria for the "component numbers", and show an equidistribution result for torsion sections of prime order. | Rick Miranda | alg-geom math.AG | August | 1,992 | https://arxiv.org/abs/alg-geom/9208004 |
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] | On the $(-1)$-curve conjecture of Friedman and Morgan | Main difference with previous version: we prove that every differentiably embedded sphere with self intersection $-1$ in a simply connected algebraic surface with $p_g >0$ is homologous to a $(-1)$-curve if $|K_{\min}|$ contains a smooth irreducible curve of genus at least 2 and $p_g$ is even or $K_{\min}^2 \not\equiv 7 \pmod8$ (here $K_{\min}$ is the canonical class of the minimal model). | Rogier Brussee | alg-geom math.AG | September | 1,992 | https://arxiv.org/abs/alg-geom/9209001 |
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] | Arrangements of Hyperplanes and Vector Bundles on $P^n$ | Any arrangement of hyperplanes in general position in $P^n$ can be regarded as a divisor with normal crossing. We study the bundles of logarithmic 1-forms corresponding to such divisors` from the point of view of classification of vector bundles on $P^n$. It turns out that all such bundles are stable. The study of jumping lines of these bundles gives a unified treatment of several classical constructions associating a curve to a collection of points in $P^n$. The main result of the paper is "Torelli theorem" which says that the collection of hyperplanes can be recovered from the isomorphism class of the corresponding logarithmic bundle unless the hyperplanes ocsulate a rational normal curve. In this latter case our construction reduces to that of secant bundles of Schwarzenberger. | I.Dolgachev and M.Kapranov | alg-geom math.AG | October | 1,992 | https://arxiv.org/abs/alg-geom/9210001 |
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] | Chow quotients of Grassmannian I | We introduce a certain compactification of the space of projective configurations i.e. orbits of the group $PGL(k)$ on the space of $n$ - tuples of points in $P^{k-1}$ in general position. This compactification differs considerably from Mumford's geometric invariant theory quotient. It is obtained by considering limit position (in the Chow variety) of the closures of generic orbits. The same result will be obtained if we study orbits of the maximal torus on the Grassmannian $G(k,n)$. We study in detail the closures of the torus orbits and their "visible contours" which are Veronese varieties in the Grassmannian. For points on $P^1$ our construction gives the Grothemdieck - Knudsen moduli space of stable $n$ -punctured curves of genus 0. The "Chow quotient" interpretation of this space permits us to represent it as a blow up of a projective space. | M.Kapranov | alg-geom math.AG | October | 1,992 | https://arxiv.org/abs/alg-geom/9210002 |
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] | The simple method of distinguishing the underlying differentiable structures of algebraic surfaces | The simplest version of the Spin-polynomial invariants of the underlying differentiable structures of algebraic surfaces were considered and the simplest arguments were used in order to distinguish the underlying smooth structures of certain algebraic surfaces. | Andrej Tyurin | alg-geom math.AG | October | 1,992 | https://arxiv.org/abs/alg-geom/9210003 |
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] | Points of Low Degree on Smooth Plane Curves | The purpose of this note is to provide some applications of Faltings' recent proof of S. Lang's conjecture to smooth plane curves. Let $C$ be a smooth plane curve defined by an equation of degree $d$ with integral coefficients. We show that for $d\ge 7$, the curve $C$ has only finitely many points whose field of definition has degree $\le d-2$ over $Q$, and that for $d\ge 8$, all but finitely many points of $C$ whose field of definition has degree $\le d-1$ over $Q$ arise as points of intersection of rational lines through rational points of $C$. | Olivier Debarre and Matthew Klassen | alg-geom math.AG | October | 1,992 | https://arxiv.org/abs/alg-geom/9210004 |
alg-geom/9210005 | [
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] | Degrees of Curves in Abelian Varieties | The degree of a curve $C$ in a polarized abelian variety $(X,\lambda)$ is the integer $d=C\cdot\lambda$. When $C$ generates $X$, we find a lower bound on $d$ which depends on $n$ and the degree of the polarization $\lambda$. The smallest possible degree is $d=n$ and is obtained only for a smooth curve in its Jacobian with its principal polarization (Ran, Collino). The cases $d=n+1$ and $d=n+2$ are studied. Moreover, when $X$ is simple, it is shown, using results of Smyth on the trace of totally positive algebraic integers, that if $d\le 1.7719\, n$, then $C$ is smooth and $X$ is isomorphic to its Jacobian. We also get an upper bound on the geometric genus of $C$ in terms of its degree. | Olivier Debarre | alg-geom math.AG | October | 1,992 | https://arxiv.org/abs/alg-geom/9210005 |
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] | Reductive group actions on K\"ahler manifolds | We prove that the action of a reductive complex Lie group on a K\"ahler manifold can be linearized in the neighbourhood of a fixed point, provided that the restriction of the action to some compact real form of the group is Hamiltonian with respect to the K\"ahler form. | Eugene Lerman and Reyer Sjamaar | alg-geom math.AG | October | 1,992 | https://arxiv.org/abs/alg-geom/9210006 |
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] | Stable pairs, linear systems and the Verlinde formula | We study the moduli problem of pairs consisting of a rank 2 vector bundle and a nonzero section over a fixed smooth curve. The stability condition involves a parameter; as it varies, we show that the moduli space undergoes a sequence of flips in the sense of Mori. As applications, we prove several results about moduli spaces of rank 2 bundles, including the Harder-Narasimhan formula and the SU(2) Verlinde formula. Indeed, we prove a general result on the space of sections of powers of the ideal sheaf of a curve in projective space, which includes the Verlinde formula. | Michael Thaddeus | alg-geom math.AG | October | 1,992 | https://arxiv.org/abs/alg-geom/9210007 |
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] | Erratum to "The Homogeneous Coordinate Ring of a Toric Variety", along with the original paper | This submission consists of two papers: 1) an erratum that corrects an error in the proof of Proposition 4.3 in my paper "The Homogeneous Coordinate Ring of a Toric Variety", and 2) the original (unchanged) version of the paper, published in 1995. The original paper introduced the homogeneous coordinate ring of a toric variety (now called the total coordinate ring or Cox ring) and gave a quotient construction. The paper also studied sheaves on a toric variety, and in Section 4 described its automorphism group. The error in the proof of Proposition 4.3 resulted from the faulty assumption that a certain set of graded endomorphisms forms a ring; rather, it is a monoid under composition. The erratum notes this error and gives a correct proof of the proposition. | David A. Cox (Amherst College) | alg-geom math.AG | October | 1,992 | https://arxiv.org/abs/alg-geom/9210008 |
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] | Elliptic Three-folds I: Ogg-Shafarevich Theory | We calculate the Tate-Shafarevich group of an elliptic three-fold $f:X\rightarrow S$ when $X$ and $S$ are regular and $f$ is flat, relating it to the Brauer group of $X$ and $S$. We show that given certain hypotheses on $f$, the Tate-Shafarevich group has the interpretation of isomorphism classes of elliptic curves over the function field of $S$ which have the same jacobian as the generic fibre of $f$, and for which there exists a relatively minimal model which has no multiple fibres. We use this to give examples of elliptic fibrations with isolated multiple fibres, and also to give a new counterexample to the Luroth problem in dimension three. This is a revised, hopefully improved, version with a few extra theorems and a few errors corrected. | I. Dolgachev and M. Gross | alg-geom math.AG | October | 1,992 | https://arxiv.org/abs/alg-geom/9210009 |
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] | Stable pairs on curves and surfaces | We describe stability conditions for pairs consisting of a coherent sheaf and a homomorphism to a fixed coherent sheaf on a projective variety. The corresponding moduli spaces are constructed for pairs on curves and surfaces. We consider two examples. The fixed sheaf is the structure sheaf or is a vector bundle on a divisor, i.e. Higgs pairs or framed bundles, resp. (unencoded version) | Daniel Huybrechts and Manfred Lehn | alg-geom math.AG | November | 1,992 | https://arxiv.org/abs/alg-geom/9211001 |
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] | Algebraic approximations of holomorphic maps from Stein domains to projective manifolds | It is shown that every holomorphic map $f$ from a Runge domain $\Omega$ of an affine algebraic variety $S$ into a projective algebraic manifold $X$ is a uniform limit of Nash algebraic maps $f_\nu$ defined over an exhausting sequence of relatively compact open sets $\Omega_\nu$ in $\Omega$. A relative version is also given: If there is an algebraic subvariety $A$ (not necessarily reduced) in $S$ such that the restriction of $f$ to $A\cap\Omega$ is algebraic, then $f_\nu$ can be taken to coincide with $f$ on $A\cap\Omega_\nu$. The main application of these results, when $\Omega$ is the unit disk, is to show that the Kobayashi pseudodistance and the Kobayashi-Royden infinitesimal metric of a quasi-projective algebraic manifold $Z$ are computable solely in terms of the closed algebraic curves in $Z$. Similarly, the $p$-dimensional Eisenman metric of a quasi-projective algebraic manifold can be computed in terms of the Eisenman volumes of its $p$-dimensional algebraic subvarieties. Another question addressed in the paper is whether the approximations $f_\nu$ can be taken to have their images contained in affine Zariski open subsets of $X$. By using complex analytic methods (pluricomplex potential theory and H\"ormander's $L^2$ estimates), we show that this is the case if $f$ is an embedding (with $\dim S<\dim X$) and if there is an ample line bundle $L$ on $X$ such that | Jean-Pierre Demailly, Laszlo Lempert and Bernard Shiffman | alg-geom math.AG | December | 1,992 | https://arxiv.org/abs/alg-geom/9212001 |
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] | On the stable rationality of $X/G$ | Let $G$ be a connected, reductive algeraic group whose Dynkin diagram contains no components of type $G_2,$ $F_4,$ $E_6,$ $E_7$ or $E_8.$ That is, all the components are of classical type. Suppose $X$ is an affine variety, and suppose $G$ acts freely on $X.$ Then $X$ and $X/G$ are stably birationally equivalent. | Amnon Neeman | alg-geom math.AG | December | 1,992 | https://arxiv.org/abs/alg-geom/9212002 |
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] | The enumeration of simultaneous higher-order contacts between plane curves | Using the Semple bundle construction, we derive an intersection-theoretic formula for the number of simultaneous contacts of specified orders between members of a generic family of degree $d$ plane curves and finitely many fixed curves. The contacts counted by the formula occur at nonsingular points of both the members of the family and the fixed curves. | Susan Jane Colley and Gary Kennedy | alg-geom math.AG | December | 1,992 | https://arxiv.org/abs/alg-geom/9212003 |
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] | Automorphisms and the K\"ahler cone of certain Calabi-Yau manifolds | For the Calabi-Yau threefolds $X$ constructed by C. Schoen as fiber products of generic rational elliptic surfaces, we show that the action of the automorphism group of $X$ on the K\"ahler cone of $X$ has a rationally polyhedral fundamental domain. The second author has conjectured that this statement will hold in general, the example presented here being the first non-trivial case in which the statement has been checked. The conjecture was motivated by the desire to use a construction of E. Looijenga to compactify certain moduli spaces which arise in the study of conformal field theory and ``mirror symmetry.'' | Antonella Grassi and David R. Morrison | alg-geom math.AG | December | 1,992 | https://arxiv.org/abs/alg-geom/9212004 |
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] | Gamma-Ray Bursts as the Death Throes of Massive Binary Stars | It is proposed that gamma-ray bursts are created in the mergers of double neutron star binaries and black hole neutron star binaries at cosmological distances. Bursts with complex profiles and relatively long durations are the result of magnetic flares generated by the Parker instability in a post-merger differentially-rotating disk. Some bursts may also be produced through neutrino-antineutrino annihilation into electrons and positrons. In both cases, an optically thick fireball of size $\sles\ 100$ km is initially created, which expands ultrarelativistically to large radii before radiating. Several previous objections to the cosmological merger model are eliminated. It is predicted that $\gamma$-ray bursts will be accompanied by a burst of gravitational radiation from the spiraling-in binary which could be detected by LIGO. | Ramesh Narayan, Bohdan Paczy\'nski, and Tsvi Piran | astro-ph | April | 1,992 | https://arxiv.org/abs/astro-ph/9204001 |
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] | Gravitational Lensing and the Variability of G | The four observables associated with gravitational lensing of distant quasars by intervening galaxies: image splittings, relative amplifications, time delays, and optical depths, provide separate measures of the strength of the gravitational constant $G$ at cosmological distances. These allow one, in principle, to factor out unknown lensing parameters to directly to probe the variation of $G$ over cosmological time. We estimate constraints on $\dot{G}$ which may be derivable by this method both now and in the future. The limits one may obtain can compete or exceed other direct limits on $\dot{G}$ today, but unfortunately extracting this information, is not independent of the effort to fix other cosmological parameters such as $H_0$ and $\Omega_0$ from lensing observations. | Lawrence Krauss and Martin White | astro-ph | April | 1,992 | https://arxiv.org/abs/astro-ph/9204002 |
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] | The Ptolemaic Gamma-Ray Burst Universe | The BATSE experiment on GRO has demonstrated the isotropic arrival directions and flat $\log N$ {\it vs.} $\log S$ of cosmic gamma-ray bursts. These data are best explained if the burst sources are distributed throughout an extended spherical Galactic halo, as previously suggested by Jennings. The halo's radius is at least 40 Kpc, and probably is more than 100 Kpc. I consider possible origins of this halo, including primordial formation and neutron stars recoiling from their birthplaces in the Galactic disc. A simple geometrical model leads to a predicted relation between the dipole and quadrupole anisotropy. I suggest that neutron stars born with low recoil become millisecond pulsars, while those born with high recoil become the sources of gamma-ray bursts; these populations are nearly disjoint. Quiescent counterparts of gamma-ray bursts are predicted to be undetectably faint. | J. I. Katz | astro-ph | April | 1,992 | https://arxiv.org/abs/astro-ph/9204003 |
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] | Expanding Photospheres of Type II Supernovae and the Extragalactic Distance Scale | We use the Expanding Photosphere Method to determine distances to 10 type II supernovae. The effects of asymmetries, extinction, and flux dilution are explored. Using empirical evidence and time-independent, spherical models which treat H and He in non-LTE, we show that blackbody corrections caused by flux dilution are small for type II supernovae in the infrared, and in the optical when their color temperatures are less than 6000~K. The extinction to a type II-P supernova can be estimated from its light curve: the uncertainty introduced into a distance measurement due to extinction is usually less than 10\%. Correcting for extinction and flux dilution we derive distances to 10 supernovae: SN 1968L, SN 1969L, SN 1970G, SN 1973R, SN 1979C, SN 1980K, SN 1987A, SN 1988A, SN 1990E, and SN 1990ae. The distance measurements span a wide range, 50 kpc to 120 Mpc, which is unique among the methods for establishing the extragalactic distance scale. The distances measured to SN 1970G in M101 and SN 1987A in the LMC are in good agreement with distances determined from Cepheid variable stars. Our distance to the Virgo Cluster, 22 +- 3 Mpc, is larger than recent distances estimates made using surface brightness fluctuations, planetary nebula luminosity functions, and the Tully-Fisher method. Using the distances determined from these type II supernovae we derive a value of $H_0 = 60 \pm 10$ km sec$^{-1}$Mpc$^{-1}$. This value is subject to errors caused by local deviations in the Hubble flow, but will soon be improved by applying the Expanding Photosphere Method to several distant type II supernovae. | B P Schmidt, R P Kirshner, R G Eastman | astro-ph | April | 1,992 | https://arxiv.org/abs/astro-ph/9204004 |
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] | Radiation Transfer in Gamma-Ray Bursts | We have calculated gamma-ray radiative transport in regions of high energy density, such as gamma-ray burst source regions, using a discrete ordinate, discrete energy group method. The calculations include two-photon pair production and annihilation, as well as three-photon pair annihilation. The radiation field itself acts as an absorbing medium, and the optical depth depends on its intensity, so the problem is intrinsically nonlinear. Spherical divergence produces effective collimation of the flux. At high optical depth the high energy ($E > 1$ MeV) portion of the emergent spectrum assumes a nearly universal form. An approximate limit is derived for the high energy flux from a gamma-ray burst source region of given size, and the implications of this limit for the distance to the March 5, 1979 event are briefly discussed. We discuss more generally the problem of very luminous bursts, and implications of Galactic halo distances for flare models. | B. J. Carrigan and J. I. Katz | astro-ph | April | 1,992 | https://arxiv.org/abs/astro-ph/9204005 |
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] | Nova Dust Nucleation: Kinetics and Photodissociation | Dust is observed to form in nova ejecta. The grain temperature is determined by the diluted nova radiation field rather than the gas kinetic temperature, making classical nucleation theory inapplicable. We used kinetic equations to calculate the growth of carbon nuclei in these ejecta. For expected values of the parameters too many clusters grew, despite the small sticking probability of atoms to small clusters, and the clusters only reached radii of about 100\AA\ when the carbon vapor was depleted. We then included the effects of cluster photodissociation by ultraviolet radiation from the nova. This suppresses nucleation, but too well, and no grains form at all. Finally we suggest that a few growing carbon nuclei may be protected from photodissociation by a sacrificial surface layer of hydrogen. | D. J. Johnson, M. W. Friedlander, J. I. Katz | astro-ph | April | 1,992 | https://arxiv.org/abs/astro-ph/9204006 |
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] | Nonstationary Gravitational Lenses and the Fermat Principle | We apply Perlick's (1990a) rigorous formulation of the Fermat principle in arbitrary spacetimes to prove the correctness of the description of gravitational lensing by gravitational waves, given in the literature using the scalar and vector formalisms. We obtain an expression for the time delay due to such nonstationary lenses; the advantage over previous papers is that Perlick's formulation of the Fermat principle is very rigorous and more suitable for practical calculations in some cases. It is also shown that ordinary moving gravitational lenses must be considered as a stationary case. | Valerio Faraoni | astro-ph | May | 1,992 | https://arxiv.org/abs/astro-ph/9205001 |
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] | Giant Molecular Cloud Formation through the Parker Instability in a Skewed Magnetic Field | The effect of the magnetic skew on the Parker instability is investigated by means of the linear stability analysis for a gravitationally stratified gas layer permeated by a horizontal magnetic field. When the magnetic field is skewed (i.e., the field line direction is a function of the height), the wavelength of the most unstable mode is $ \lambda \; \sim \; 10 H $ where $ H $ is the pressure scale height. The growth rate of the short wavelength modes is greatly reduced when the gradient in the magnetic field direction exceeds 0.5 radian per scale height. Our results indicate that the Parker instability in a skewed magnetic field preferentially forms large scale structures like giant molecular clouds. | T. Hanawa, R. Matsumoto and K. Shibata | astro-ph | May | 1,992 | https://arxiv.org/abs/astro-ph/9205002 |
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] | Particle Acceleration in (by) Accretion Discs | I present a model for acceleration of protons by the second-order Fermi process acting on randomly scrambled magnetic flux arches above an accretion disc. The accelerated protons collide with thermal protons in the disc, producing degraded energetic protons, charged and neutral pions, and neutrons. The pions produce gamma-rays by spontaneous decay of $\pi^0$ and by bremsstrahlung and Compton processes following the decay of $\pi^\pm$ to $e^\pm$. | J. I. Katz | astro-ph | May | 1,992 | https://arxiv.org/abs/astro-ph/9205003 |
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] | The Spatial Distribution of Nearby Galaxy Clusters in the Northern and Southern Galactic Hemispheres | We compare the spatial distributions of galaxy clusters in the northern and southern galactic hemispheres, and the Abell and ACO clusters distributions. We perform a statistical (correlation and cluster) analysis of a sample of Abell and ACO galaxy clusters in the southern galactic hemisphere. We compare these results with a symmetric sample at northern galactic latitude taken from Postman et al. (1992). For the northern sample, we substantially confirm the results of Postman et al. We find that the two-point spatial correlation function of northern and southern clusters is comparable, with mean correlation length 19.6 Mpc and slope -1.8 positive up to about 45 Mpc. Percolation properties are remarkably similar in the northern and southern cluster samples. We give also a catalog of superclusters. In the south galactic hemisphere the main feature is a very rich, extended supercluster in the Horologium region at a redshift 0.06, near to a large void. | A. Cappi & S. Maurogordato | astro-ph | May | 1,992 | https://arxiv.org/abs/astro-ph/9205004 |
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] | Chaotic Dark Matter | A very weakly coupled scalar field with mass $m$ and initial vacuum expectation value $V$ will provide enough mass to close the universe provided $V\simeq (3\times 10^8\gev)(100\gev/m)^{1/4}$. We discuss possible models in which such a field could arise. | R. Rangarajan and M. Srednicki | astro-ph | May | 1,992 | https://arxiv.org/abs/astro-ph/9205005 |
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] | Can the Quark-Gluon Plasma in the Early Universe be supercooled? | The quark-hadron phase transition in the early universe can produce inhomogeneities in the distribution of nucleons, which in turn affect the primordial nucleosynthesis. In all the investigations of this problem it has been assumed that the degree of supercooling of the quark-gluon plasma after the phase transition is large enough to produce a significant rate of nucleation of hadrons. Using the latest results of finite temperature lattice QCD and the finite size scaling theory, we argue that the degree of supercooling is in fact extremely small and hence the nucleation rate is negligible. | B. Banerjee and R. V. Gavai | astro-ph hep-lat | May | 1,992 | https://arxiv.org/abs/astro-ph/9205006 |
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] | Electroweak Baryogenesis with Electroweak Strings | If stable electroweak strings are copiously produced during the electroweak phase transition, they may contribute significantly to the presently observed baryon to entropy ratio of the Universe. This analysis establishes the feasibility of implementing an electroweak baryogenesis scenario without a first order phase transition. | Robert H. Brandenberger (Brown) and Anne-Christine Davis (DAMTP, Cambridge) | astro-ph hep-ph | June | 1,992 | https://arxiv.org/abs/astro-ph/9206001 |
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] | Primordial Nucleosynthesis and the Abundances of Beryllium and Boron | The ability to now make measurements of Be and B as well as put constraints on \lisix\ abundances in metal-poor stars has led to a detailed reexamination of Big Bang Nucleosynthesis in the $A\groughly6$ regime. The nuclear reaction network has been significantly expanded with many new rates added. It is demonstrated that although a number of $A>7$ reaction rates are poorly determined, even with extreme values chosen, the standard homogeneous model is unable to produce significant yields (Be/H and B/H $<10^{-17}$ when $A\le7$ abundances fit) above $A=7$ and the \liseven/\lisix\ ratio always exceeds 500. We also preliminarily explore inhomogeneous models, such as those inspired by a first order quark-hadron phase transition, where regions with high neutron/proton ratios can allow some leakage up to $A>7$. However models that fit the $A\le7$ abundances still seem to have difficulty in obtaining significant $A>7$ yields. | David Thomas, David N. Schramm, Keith A. Olive, Brian D. Fields | astro-ph | June | 1,992 | https://arxiv.org/abs/astro-ph/9206002 |
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] | Gamma Ray Signatures from Ordinary Cosmic Strings | We calculate the flux of ultra high energy photons from individual ordinary (i.e. non-superconducting) cosmic strings and compare the results with the sensitivity of current and proposed TeV and EeV telescopes. Our calculations give only upper limits for the gamma ray flux, since the source of the photons, jets from particle production at cusps, may be weakened by back reaction effects. For the usual cosmic distribution of strings, the predicted bursts from strings with the value of mass per unit length associated with galaxy formation or light strings may just be detectable. A diffuse gamma ray background from light strings may also be seen by the Fly's Eye detector at above $7 \times 10^{10}$ GeV. | Jane H. MacGibbon (NASA/Goddard) and Robert H. Brandenberger (Brown) | astro-ph hep-ph | June | 1,992 | https://arxiv.org/abs/astro-ph/9206003 |
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] | Dynamics of the Intermediate-Age Elliptical LMC Cluster NGC 1978 | In this paper we investigate the internal dynamics of the LMC cluster NGC 1978 through the use of Photometric (CCD images) and kinematic (stellar radial velocities) data. We apply a variety of dynamical models to this data, including multi-mass King-Michie models and rotating and non-rotating oblate spheroid models. We discuss the cluster mass-to-light ratio and place constraints on the cluster mass function. | Philippe Fischer, Douglas L. Welch, and Mario Mateo | astro-ph | June | 1,992 | https://arxiv.org/abs/astro-ph/9206004 |
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0.9845413565635681,
0.25856566429138184,
0.238625168800354,
-0.399692565202713
] | Entropy of a Classical Stochastic Field and Cosmological Perturbation | We propose a general definition of nonequilibrium entropy of a classical stochastic field. As an example of particular interest in cosmology we apply this definition to compute the entropy of density perturbations in an inflationary Universe. On the scales of structures in the Universe, the entropy of density perturbations dominates over the statistical fluctuations of the entropy of cosmic microwave photons, indicating the relevance of the entropy of density fluctuations for structure formation. | R. Brandenberger (Brown), V. Mukhanov (ETH Zuerich) and T. Prokopec (Brown) | astro-ph hep-ph | June | 1,992 | https://arxiv.org/abs/astro-ph/9206005 |
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] | Cosmic Microwave Background Probes Models of Inflation | Inflation creates both scalar (density) and tensor (gravity wave) metric perturbations. We find that the tensor mode contribution to the CMB anisotropy on large-angular scales can only exceed that of the scalar mode in models where the spectrum of perturbations deviates significantly from scale invariance (e.g., extended and power-law inflation models and extreme versions of chaotic inflation). If the tensor mode dominates at large-angular scales, then the value of $\Delta T/T$ predicted on $1^\circ$ is less than if the scalar mode dominates, and, for cold dark matter models, $b>1$ can be made consistent with the COBE DMR results. | R.L. Davis, H.M. Hodges, G.F. Smoot, P.J. Steinhardt, M.S. Turner | astro-ph hep-ph | July | 1,992 | https://arxiv.org/abs/astro-ph/9207001 |
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] | Graceful Exit in Extended Inflation and Implications for Density Perturbations | Two qualitatively different modes of ending superluminal expansion are possible in extended inflation. One mode, different from the one envoked in most extended models to date, easily avoids making big bubbles that distort the cosmic microwave background radiation (CMBR). In this mode, the spectrum of density fluctuations is found to be scale-free, $P(k) \propto k^n$, where $n$ might lie anywhere between 0.5 and 1.0 (whereas, previously, it appeared that the range $1.0> n \gtsim 0.84$ was disallowed). | R. Crittenden and Paul J. Steinhardt | astro-ph hep-ph | July | 1,992 | https://arxiv.org/abs/astro-ph/9207002 |
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] | The Angular Dependence of the Three-Point Correlation Function of the Cosmic Microwave Background Radiation as Predicted by Inflationary Cosmologies | Inflationary models predict a definite, model independent, angular dependence for the three-point correlation function of $\Delta T/T$ at large angles (greater than $\sim 1^\circ$) which we calculate. The overall amplitude is model dependent and generically unobservably small, but may be large in some specific models. We compare our results with other models of nongaussian fluctuations. | Toby Falk, Raghavan Rangarajan, and Mark Srednicki | astro-ph hep-ph | August | 1,992 | https://arxiv.org/abs/astro-ph/9208001 |
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] | Dependence of Density Perturbations on the Coupling Constant in a Simple Model of Inflation | In the standard inflationary scenario with inflaton potential $V(\Phi)=M^4-{1\over4}\lambda\Phi^4$, the resulting density perturbations $\delta\rho/\rho$ are proportional to $\lambda^{1/2}$. Upper bounds on $\delta\rho/\rho$ require $\lambda < 10^{-13}$. Ratra has shown that an alternative treatment of reheating results in $\delta\rho/\rho \propto \lambda^{-1}$, so that an upper bound on $\delta\rho/\rho$ does not put an obvious upper bound on $\lambda$. We verify that $\delta\rho/\rho \propto \lambda^{-1}$ is indeed a possibility, but show that $\lambda < 10^{-13}$ is still required. | Toby Falk, Raghavan Rangarajan, and Mark Srednicki | astro-ph | August | 1,992 | https://arxiv.org/abs/astro-ph/9208002 |
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] | The Probability for Formation of Collapsing Textures and Texture Knots | Global textures are interesting because they are promising candidates for seeds in the structure formation of the universe. The important configurations are those who will be able to collapse. The type of configurations that I will consider are half knots and true knots. I define a half knot as one that covers more than a half-$S^3$, and a true knot as a configuration that covers the whole of $S^3$. Configurations that are half knots will be able to collapse, a new argument for this collapse criterion is given in this paper. I also give some critical remarks on the method of using the total winding number as a criterion for identifying a knot. I propose another more direct method and make use of it when I estimate the probability for formation of both true and half knots by numerical simulations.Taking into account the chance of annihilation the probability for collapse is found to be in the interval $p_{coll} \in [0.01,0.04]$. In the skyrmion picture of hadrons the investigations of formation of true knots are important, and some implications of my result on the predictions of a "topological" theory of baryon production in jets are discussed. | Stefan {\AA}minneborg (Stockholm University) | astro-ph hep-th | August | 1,992 | https://arxiv.org/abs/astro-ph/9208003 |
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] | Constraints on radiative decay of the 17-keV neutrino from COBE Measurements | It is shown that, for a nontrivial radiative decay channel of the 17-keV neutrino, the photons would distort the microwave background radiation through ionization of the universe. The constraint on the branching ratio of such decays from COBE measurements is found to be more stringent than that from other considerations. The limit on the branching ratio in terms of the Compton $y$ parameter is $B_\gamma < 1.5 \times 10^{-7} ({\tau_\nu \over 10^{11} sec})^{0.45} ({y \over 10^{-3}})^{1.11} h^{-1}$ for an $\Omega=1, \Omega_b=0.1$ universe. | Biman B. Nath | astro-ph hep-ph | August | 1,992 | https://arxiv.org/abs/astro-ph/9208004 |
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] | The Last Three Minutes: Issues in Gravitational Wave Measurements of Coalescing Compact Binaries | Gravitational-wave interferometers are expected to monitor the last three minutes of inspiral and final coalescence of neutron star and black hole binaries at distances approaching cosmological, where the event rate may be many per year. Because the binary's accumulated orbital phase can be measured to a fractional accuracy $\ll 10^{-3}$ and relativistic effects are large, the waveforms will be far more complex, carry more information, and be far harder to model theoretically than has been expected. Theorists must begin now to lay a foundation for extracting the waves' information. | Curt Cutler, Theocharis A. Apostolatos, Lars Bildsten, Lee Samuel Finn, Eanna E. Flanagan, Daniel Kennefick, Dragoljubov M... | astro-ph gr-qc | August | 1,992 | https://arxiv.org/abs/astro-ph/9208005 |
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