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Algebraic Geometry papers — page 13

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Dual varieties and the duality of the second fundamental form
First, we consider a compact real-analytic irreducible subvariety M in a sphere and its dual variety M. We explain that two matrices of the second fundamental forms for both varieties M…
Tohsuke UrabeFeb 3, 1997
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Residues and Resultants
Resultants, Jacobians and residues are basic invariants of multivariate polynomial systems. We examine their interrelations in the context of toric geometry. The global residue in the torus, studied…
Eduardo Cattani, Alicia Dickenstein, Bernd SturmfelsJan 31, 1997
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Counting rational curves on K3 surfaces
The aim of these notes is to explain the remarkable formula found by Yau and Zaslow to express the number of rational curves on a K3 surface. Projective K3 surfaces fall into countably many families…
Arnaud BeauvilleJan 30, 1997
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Exemples de composantes irréductibles et non réduites du schéma de Hilbert des courbes lisses et connexes de P3 (II)
Soit Hd,g le schéma de Hilbert des courbes lisses et connexes de degré d et genre g de l'espace projectif P3 sur un corps k algébriquement clos de caractéristique nulle. Le…
Said AzzizJan 29, 1997
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Heights and Geometric Invariant Theory
Let K be a number field, be its ring of integers. We introduce the notion of compactified representation of GLN() and, we see how to associate to a hermitian vector bundle over…
Carlo GasbarriJan 29, 1997
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A mirror theorem for toric complete intersections
We prove a generalized mirror conjecture for non-negative complete intersections in symplectic toric manifolds. Namely, we express solutions of the PDE system describing quantum cohomology of such a…
Alexander GiventalJan 27, 1997
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A remark on an algebraic Riemann-Roch formula for flat bundles
We propose an algebraic Riemann-Roch formula for moving flat bundles on contant families in characteristic zero with values in the ring of algebraic differential characters. This formula lifts…
Hélène EsnaultJan 27, 1997
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Geometry of cohomology support loci II: integrability of Hitchin's map
In very rough terms, the main theorem is that the set, which consists of semistable vector bundles with trivial rational Chern classes and nontrivial kth cohomology on a smooth complex projective…
Donu ArapuraJan 26, 1997
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Families of K3 surfaces
We use automorphic forms to prove that a compact family of Kaehler K3 surfaces with constant Picard number is isotrivial.
Richard E. Borcherds, Ludmil Katzarkov, Tony Pantev et al.Jan 26, 1997
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A Prym construction for the cohomology of a cubic hypersurface
Mumford defined a natural isomorphism between the intermediate jacobian of a conic-bundle over P2 and the Prym variety of a naturally defined étale double cover of the discrminant curve of the…
E. IzadiJan 25, 1997
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K3 surfaces with interesting groups of automorphisms
By the fundamental result of I.I. Piatetsky-Shapiro and I.R. Shafarevich (1971), the automorphism group Aut(X) of a K3 surface X over C and its action on the Picard lattice SX are prescribed by the…
Viacheslav V. NikulinJan 24, 1997
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Subvarieties of SUC(2) and 2θ-divisors in the Jacobian
We explore some of the interplay between Brill-Noether subvarieties of the moduli space SUC(2,K) of rank 2 bundles with canonical determinant on a smooth projective curve and 2θdivisors, via the…
W. M. Oxbury, C. Pauly, E. PreviatoJan 23, 1997
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On the singularities of the theta divisors on Jacobians
We study the intersection cohomology of the theta divisors on Jacobians of nonhyperelliptic curves.
P. Bressler, J. -L. BrylinskiJan 22, 1997
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Adelic Formulas for Gamma- and Beta-functions in Algebraic Numbers Fields
On the basis of analysis on the adele ring of any algebraic numbers field (Tate's formula) a regularization for divergent adelic products of gamma- and beta-functions for all completions of this…
V. S. VladimirovJan 20, 1997
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On Hitchin's Connection
The aim of this paper is to give an explicit expression for Hitchin's connection in the case of rank 2 bundles with trivial determinant over curves of genus 2. We recall the definition of this…
Bert van Geemen, Aise Johan de JongJan 18, 1997
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On the cone of divisors of Calabi-Yau fiber spaces
We prove some version of Morrison's conjecture on the cone of divisors for Calabi-Yau fiber spaces with non-trivial base pace whose total space is 3-dimensional.
Yujiro KawamataJan 13, 1997
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Quotients par des groupes non réductifs et variétés de modules de complexes
I give a way to construct moduli spaces of complexes, as quotients of open subsets of the space of all complexes by the product of the groups of automorphisms of the terms.
J. -M. DrezetJan 9, 1997
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Simultaneous minimal model of homogeneous toric deformation
For a flat family of Du Val singularities, we can take a simultaneous resolution after finite base change. It is an interesting problem to consider this analogy for a flat family of higher…
D. MatsushitaJan 9, 1997
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Hodge numbers attached to a polynomial map
Given a polynomial map f: Cn+1 C, one can attach to it a geometrical variation of mixed Hodge structures (MHS) which gives rise to a limit MHS. The equivariant Hodge numbers of this…
Ricardo Garcia, Andras NemethiJan 8, 1997
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A smooth surface in P4 not of general type has degree at most 46
This is the continuation of papers by Braun and Floystad, Cook, Braun and Cook. We use Generic Initial Ideal Theory in conjunction with Liaison Theory to further restrict the possible generic initial…
M. CookJan 4, 1997
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A smooth surface in P4 not of general type has degree at most 66
We continue the work of Braun and Floystad, and Cook bounding the degree of smooth surfaces in P4 not of general type using generic initial ideal theory.
R. Braun, M. CookJan 4, 1997
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Jacobi forms and the structure of Donaldson invariants for 4-manifolds with b+=1
We prove structure theorems for the Donaldson invariants of 4-manifolds with b+=1, similar to those of Kronheimer and Mrowka in the case b+>1: We show that for a 4-manifold with b+=1 and two…
Lothar Göttsche, Don ZagierDec 26, 1996
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Is a linear space contained in a variety? - On the number of derivatives needed to tell
Let Xn⊂ Cn+a or Xn⊂ Pn+a be a patch of an analytic submanifold of an affine or projective space, let x∈ X be a general point, and let Lk be a linear space of dimension k…
J. M. LandsbergDec 24, 1996
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Effective base point freeness on a normal surface
This treats the base-point-freeness of the adjoint bundles on normal surfaces with a boundary. This is an extension of the non-relative version of the theorem of Ein-Lazarsfeld-Masek and the theorem…
Takeshi KawachiDec 20, 1996
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Weil classes on abelian varieties
Consider a complex abelian variety X on which a field F acts. Generalizing a construction of A. Weil, one associates to this a subspace WF of the cohomology of X, which we call the space of Weil…
B. J. J. Moonen, Yu. G. ZarhinDec 19, 1996
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