On parametrizing exceptional tangent cones to Prym theta divisors

  title={On parametrizing exceptional tangent cones to Prym theta divisors},
  author={Roy Smith and Robert Varley},
  journal={Transactions of the American Mathematical Society},
  • 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… 



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


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


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

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