On parametrizing exceptional tangent cones to Prym theta divisors

@article{Smith2016OnPE,
  title={On parametrizing exceptional tangent cones to Prym theta divisors},
  author={Roy Smith and Robert Varley},
  journal={Transactions of the American Mathematical Society},
  year={2016},
  volume={369},
  pages={3763-3798}
}
  • Roy Smith, R. Varley
  • Published 7 December 2016
  • Mathematics
  • Transactions of the American Mathematical Society
The theta divisor of a Jacobian variety is parametrized by a smooth divisor variety via the Abel map, with smooth projective linear fibers. Hence the tangent cone to a Jacobian theta divisor at any singularity is parametrized by an irreducible projective linear family of linear spaces normal to the corresponding fiber. The divisor variety X parametrizing a Prym theta divisor Ξ on the other hand, is singular over any exceptional point, hence although the fibers of the Abel Prym map are still… 

References

SHOWING 1-10 OF 29 REFERENCES

Tangent cones to discriminant loci for families of hypersurfaces

A deformation of a variety with (nonisolated) hypersurface singularities, such as a projective hypersurface or a theta divisor of an abelian variety, determines a rational map of the singular locus

Prym Varieties I

Prym varieties and the Schottky problem

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

Singularities of the Prym theta divisor

For the Jacobian of a curve, the Riemann singularity theorem gives a geometric interpretation of the singularities of the theta divisor in terms of special linear series on the curve. This paper

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

The Prym Torelli problem : an update and a reformulation as a question in birational geometry

Table of Contents 0. Introduction 1. The Prym Torelli problem andDonagìs conjecture 2. Thè`base locus of quadrics`` method for Jacobians Enriques theorem Riemann singularities package Green`s rank 4

A Riemann singularities theorem for Prym theta divisors, with applications

Let (P,Ξ) be the naturally polarized model of the Prym variety associated to the etale double cover π : C → C of smooth connected curves, where Ξ ⊂ P ⊂ Pic2g−2(C), and g(C) = g. If L is any “non

On the Geometry of a Theorem of Riemann

Let C be a smooth complete algebraic curve. Let I: C-+J be an universal abelian integral of C into its Jacobian J. Furthermore, let I(i): C(i) J be the mapping sending a point c1 + *-+ ci in the ith

INTERSECTION THEORY

I provide more details to the intersection theoretic results in [1]. CONTENTS 1. Transversality and tubular neighborhoods 1 2. The Poincaré dual of a submanifold 4 3. Smooth cycles and their

Geometry of algebraic curves

TLDR
This chapter discusses Brill-Noether theory on a moving curve, and some applications of that theory in elementary deformation theory and in tautological classes.