Prym varieties and the Schottky problem

@article{Beauville1977PrymVA,
  title={Prym varieties and the Schottky problem},
  author={Arnaud Beauville},
  journal={Inventiones mathematicae},
  year={1977},
  volume={41},
  pages={149-196}
}
  • A. Beauville
  • Published 1 June 1977
  • Mathematics
  • Inventiones mathematicae
be the moduli space of principally polarized abelian varieties of dimension g, Jg c ~q/g the locus of Jacobians. The problem is to find explicit equations for Jg (or rather its closure Jg) in s/g. In their beautiful paper [A-M], Andreotti and Mayer prove that Jg is an irreducible component of the locus N~_ 4 of principally polarized abelian varieties (A, O) with dim Sing O > g 4 . Then they give a procedure to write "explicit" equations for N~_ 4. There is no hope that Jg be equal to Ng_ 4… 
Singularities of theta divisors and the geometry of A_5
We study the codimension two locus H in A_g consisting of principally polarized abelian varieties whose theta divisor has a singularity that is not an ordinary double point. We compute the class of H
Prym varieties and the Schottky problem for cubic threefolds
This paper extends joint work with R. Friedman to show that the closure of the locus of intermediate Jacobians of smooth cubic threefolds, in the moduli space of principally polarized abelian
On subvarieties of abelian varieties
Let A be a complete nonsingular algebraic curve of genus n over IF. The Jacobian J(A) has the standard subvarieties Wj={a I +...ae: areA}, considering A as embedded in J(A), and PoincarCs formula
Syzygies of torsion bundles and the geometry of the level l modular variety over Mg
We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a
On the Tannaka group attached to the Theta divisor of a generic principally polarized abelian variety
To any closed subvariety Y of a complex abelian variety one can attach a reductive algebraic group G which is determined by the decomposition of the convolution powers of Y via a certain Tannakian
PRYM VARIETIES: THEORY AND APPLICATIONS
In this paper the author determines when the principally polarized Prymian of a Beauville pair satisfying a certain stability type condition is isomorphic to the Jacobian of a nonsingular curve. As
J an 2 00 1 Degenerations of Prym Varieties
Let (C, ι) be a stable curve with an involution. Following a classical construction , one can define its Prym variety P , which in this case turns out to be a semi-abelian group variety and usually
THE NON-ABELIAN BRILL-NOETHER DIVISOR ON M 13 AND THE KODAIRA DIMENSION OF R 13
A BSTRACT . The paper is devoted to highlighting several novel aspects of the moduli space of curves of genus 13 , the first genus g where phenomena related to K 3 surfaces no longer govern the
Ju l 2 00 0 THE HODGE CONJECTURE FOR GENERAL PRYM VARIETIES
We work over C, the field of complex numbers. The Prym variety of a double cover C → D of a smooth connected projective curve D by a smooth connected curve C is defined (see [7]) as the identity
Geometry of theta divisors --- a survey
We survey the geometry of the theta divisor and discuss various loci of principally polarized abelian varieties (ppav) defined by imposing conditions on its singularities. The loci defined in this
...
...

References

SHOWING 1-10 OF 16 REFERENCES
On Products and Algebraic Families of Jacobian Varieties
1. The first theorem of this paper (? 2) is an extension to products of jacobian varieties of Matsusaka's characterization of a jacobian variety [6, Th. 3]. As a corollary (? 3) we obtain a result
Stable and unitary vector bundles on a compact Riemann surface
Let X be a compact Riemann surface of genus g _ 2. A holomorphic vector bundle on X is said to be unitary if it arises from a unitary representation of the fundamental group of X. We prove in this
Equations Defining Abelian Varieties
We shall start this chapter by proving “theta relations,” i.e., relations between theta functions. More precisely, we shall be interested in polynomial relations between θm(τ, z), θm(τ, 0) with
Geometric Invariant Theory
“Geometric Invariant Theory” by Mumford/Fogarty (the first edition was published in 1965, a second, enlarged edition appeared in 1982) is the standard reference on applications of invariant theory to
On Petri's analysis of the linear system of quadrics through a canonical curve
where S*H°(I2) denote the symmetric algebra of H°(f2), is surjective. (2) The kernel I of ~p is generated by its elements of degree 2 and of degree 3. (3) I is generated by its elements of degree 2
On the equations defining abelian varieties. III
The Göttingen State and University Library provides access to digitized documents strictly for noncommercial educational, research and private purposes and makes no warranty with regard to their use
On period relations for abelian integrals on algebraic curves
L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions
The irreducibility of the space of curves of given genus
© Publications mathematiques de l’I.H.E.S., 1969, tous droits reserves. L’acces aux archives de la revue « Publications mathematiques de l’I.H.E.S. » (http://www.
Theta characteristics of an algebraic curve
© Gauthier-Villars (Editions scientifiques et medicales Elsevier), 1971, tous droits reserves. L’acces aux archives de la revue « Annales scientifiques de l’E.N.S. » (http://www.
Introduction to Grothendieck Duality Theory
Preface.- Study of ?X.- Completions, primary decomposition and length.- Depth and dimension.- Duality theorems.- Flat morphisms.- Etale morphisms.- Smooth morphisms.- Curves.
...
...