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Algebraic Geometry papers — page 3

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Real Algebraic Surfaces
These are the notes for my lectures at the Trento summer school held September 1997. The aim of the lectures is to provide an introduction to real algebraic surfaces using the minimal model program.…
János KollárDec 2, 1997
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Coupled Contact Systems and Rigidity of Maximal Dimensional Variations of Hodge Structure
In this article we prove that locally Griffiths' horizontal distribution on the period domain is given by a generalized version of the familiar contact differential system. As a consequence of…
Richard MayerNov 30, 1997
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On the Euler Characteristic of Generalized Kummer Varieties
We apply the Yau-Zaslow-Beauville method to compute the Euler characteristic of the generalized Kummer varieties attached to a complex abelian surface (a calculation also done by Goettsche and…
Olivier DebarreNov 28, 1997
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Minimal discrepancies of hypersurface singularities
We give an upper bound for the minimal discrepancies of hypersurface singularities. As an application, we show that Shokurov's conjecture is true for log-terminal threefolds.
Vladimir MasekNov 26, 1997
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Uniform Zariski's Theorem On Fundamental Groups
The Zariski theorem says that for every hypersurface in a complex projective (resp. affine) space of dimension at least 3 and for every generic plane in the projective (resp. affine) space the…
Shulim KalimanNov 25, 1997
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On the classification of hyperbolic root systems of the rank three. Part I
It was recently understood that from the point of view of automorphic Lorentzian Kac-Moody algebras and some aspects of Mirror Symmetry, interesting hyperbolic root systems should have restricted…
Viacheslav V. NikulinNov 25, 1997
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The enumerative geometry of K3 surfaces and modular forms
We prove the conjectures of Yau-Zaslow and Gottsche concerning the number curves on K3 surfaces. Specifically, let X be a K3 surface and C be a holomorphic curve in X representing a primitive…
Jim Bryan, Naichung Conan LeungNov 24, 1997
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Quantum cohomology of the moduli space of stable bundles over a Riemann surface
We determine the quantum cohomology of the moduli space of odd degree rank two stable vector bundles over a Riemann surface Σ of any genus. This work together with dg-ga/9710029 prove that this…
Vicente MuñozNov 24, 1997
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Classification of Exceptional Complements: Elliptic Curve Case
We classify the log del Pezzo surface (S,B) of rank 1 with no 1-,2-,3-,4-, or 6-complements with the additional condition that B has one irreducible component C which is an elliptic curve, and that C…
Terutake AbeNov 24, 1997
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On moduli spaces of 4- or 5-instanton bundles
We study the scheme of multi-jumping lines of an n-instanton bundle mainly for n≤ 5. We apply it to prove the irreducibility and smoothness of the moduli space of 5-instanton. Some particular…
F. HanNov 21, 1997
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Mathematical Instantons In Characteristic Two
On P3, we show that mathematical instantons in characteristic two are unobstructed. We produce upper bounds for the dimension of the moduli space of stable rank two bundles on P3 in characteristic…
A. P. RaoNov 20, 1997
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Cycles on Siegel 3-folds and derivatives of Eisenstein series
We consider the Siegel modular variety of genus 2 and a p-integral model of it for a good prime p>2, which parametrizes principally polarized abelian varieties of dimension two with a level…
S. Kudla, M. RapoportNov 20, 1997
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Equations of the moduli of pointed curves in the infinite Grassmannian
The main result of this paper is the explicit computation of the equations defining the moduli space of triples (C,p,z) (where C is an integral and complete algebraic curve, p a smooth rational…
J. M. Muñoz Porras, F. J. Plaza MartínNov 19, 1997
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Cellular Resolutions of Monomial Modules
We construct a canonical free resolution for arbitrary monomial modules and lattice ideals. This includes monomial ideals and defining ideals of toric varieties, and it generalizes our joint results…
Dave Bayer, Bernd SturmfelsNov 19, 1997
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A geometric approach to the fundamental lemma for unitary groups
We consider from a geometric point of view the conjectural fundamental lemma of Langlands and Shelstad for unitary groups over a local field of positive characteristic. We introduce projective…
G. Laumon, M. RapoportNov 19, 1997
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Semistable reduction in characteristic 0 for families of surfaces and three-folds
Let F:X->B be a morphism of varieties in characteristic zero. The problem of semistable reduction of F was stated as a problem in the combinatorics of polyhedral complexes by Abramovich and Karu…
Kalle KaruNov 17, 1997
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Stringy Hodge numbers and Virasoro algebra
Let X be an arbitrary smooth n-dimensional projective variety. It was discovered by Libgober and Wood that the product of the Chern classes c1(X)cn-1(X) depends only on the Hodge numbers of…
Victor V. BatyrevNov 16, 1997
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On a conjecture of Lange
Let C be a projective smooth curve of genus g> 1. Let E be a vector bundle of rank r on C. For each integer r'<r, associate to E the invariant sr'(E)=r'deg(E)-rdeg(E') where…
B. Russo, M. Teixidor i BigasNov 14, 1997
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On the theta divisor of SU(2,1)
Let SU(2,1) be the moduli space of stable rank two vector bundles having fixed determinant of odd degree over a compact Riemann surface C. In this paper it is shown that the Theta divisor of SU(2,1)…
Sonia Brivio, Alessandro VerraNov 13, 1997
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Boundary Manifolds of Line Arrangements
In this paper we describe the complement of real line arrangements in the complex plane in terms of the boundary three-manifold of the line arrangement. We show that the boundary manifold of any line…
Eriko HironakaNov 12, 1997
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Topological Triviality of μ-constant Deformations of Type f(x) + tg(x)
We show that every μ-constant family of isolated hypersurface singularities of type f(x) + tg(x), where t is a parameter, is topologically trivial. In the proof we construct explicitely a vector…
Adam ParusinskiNov 11, 1997
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First quantum correction for the moduli space of stable bundles over a Riemann surface
We compute some Gromov-Witten invariants of the moduli space of odd degree rank two stable vector bundles over a Riemann surface of any genus. Next we find the first correction term for the quantum…
Vicente MuñozNov 11, 1997
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A conjectural generating function for numbers of curves on surfaces
I give a conjectural generating function for the numbers of δ-nodal curves in a linear system of dimension δ on an algebraic surface. It reproduces the results of Vainsencher for the case $δ…
Lothar GoettscheNov 11, 1997
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Constructing curves over finite fields with many points by solving linear equations
In this note is we exhibit an elementary method to construct explicitly curves over finite fields with many points. Despite its elementary character the method is very efficient and can be regarded…
Gerard van der Geer, Marcel van der VlugtNov 10, 1997
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Semiinfinite Flags. II. Local and Global Intersection Cohomology of Quasimaps' Spaces
For a simple algebraic group G we study the space Q of Quasimaps from the projective line C to the flag variety of G. We prove that the global Intersection Cohomology of Q carries a natural…
Boris Feigin, Michael Finkelberg, Alexander Kuznetsov et al.Nov 8, 1997
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