Related papers: Coble duality for Jacobian Kummer fourfolds

In the paper "The universal Kummer threefold", Q. Ren, S. Sam, G. Schrader, and B. Sturmfels (arXiv:1208.1229), conjectured equations for the universal Kummer variety in genus 3 case. Though, most of these equations are obtained from the…

Let $C$ be a curve of genus two. We denote by $SU_C(3)$ the moduli space of semi-stable vector bundles of rank 3 and trivial determinant over $C$, and by $J^d$ the variety of line bundles of degree $d$ on $C$. In particular, $J^1$ has a…

We examine \'etale covers of genus two curves that occur in the linear system of a polarizing line bundle of type $(1,d)$ on a complex abelian surface. We give results counting fixed points of involutions on such curves as well as…

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 proves an analogous theorem for Prym…

We study special subvarieties, i.e., subvarieties containing a dense subset of CM points, of the moduli space $A_5$ of principally polarized abelian varieties of dimension five, generically contained in the locus of intermediate Jacobians…

We explore some of the interplay between Brill-Noether subvarieties of the moduli space SU_C(2,K) of rank 2 bundles with canonical determinant on a smooth projective curve and 2\theta divisors, via the inclusion of the moduli space into…

This paper deals with singularities of genus 2 curves on a general (d_1,d_2)-polarized abelian surface (S,L). In analogy with Chen's results concerning rational curves on K3 surfaces [Ch1,Ch2], it is natural to ask whether all such curves…

We construct two pencils of bielliptic curves of genus three and genus five. The first pencil is associated with a general abelian surface with a polarization of type $(1,2)$. The second pencil is related to the first by an unramified…

The paper discusses geometric and computational aspects associated with $(n,n)$-isogenies for principally polarized Abelian surfaces and related Kummer surfaces. We start by reviewing the comprehensive Theta function framework for…

We give a method for finding rational equations of genus 2 curves whose jacobians are abelian varieties $A_f$ attached by Shimura to normalized newforms $f \in S_2( \Gamma_0(N))$. We present all the curves corresponding to principally…

We discuss several geometric features of a Kummer surface associated with a (1,2)-polarized abelian surface defined over the field of complex numbers. In particular, we show that any such Kummer surface can be modeled as the double cover of…

We study the enumerative geometry of algebraic curves on abelian surfaces and threefolds. In the abelian surface case, the theory is parallel to the well-developed study of the reduced Gromov-Witten theory of K3 surfaces. We prove complete…

We prove that the generic point of a Hilbert modular four-fold is not a Jacobian. The proof uses degeneration techniques and is independent of properties of the mapping class group used in preceding papers on locally symmetric subvarieties…

We study Jacobian varieties for tropical curves. These are real tori equipped with integral affine structure and symmetric bilinear form. We define tropical counterpart of the theta function and establish tropical versions of the…

We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian…

We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of…

We explicitly find an equation and a projective embedding of the Kummer surface associated to the Jacobian of a curve of genus 2 given by an equation of the form y^2 + h(x)y = f(x) over an arbitrary ground field as well as several maps that…

We study the 2-parity conjecture for Jacobians of hyperelliptic curves over number fields. Under some mild assumptions on their reduction, we prove the conjecture over quadratic extensions of the base field. The proof proceeds via a…

Using a new type of Jacobi field estimate we will prove a duality theorem for singular Riemannian foliations in complete manifolds of nonnegative sectional curvature.

In this paper we consider cubic 4-folds containing a plane whose discriminant curve is a reduced nodal plane sextic. In particular, we describe the singular points of such cubic 4-folds and we give an estimate of the rank of the free…