Related papers: The universal abelian variety over A_5

Let A be the moduli space of principally polarized abelian varieties of dimension 4 over an algebraically closed field k of characteristic different from 2,3. It is proved that the universal principally polarized abelian variety over A, as…

We compute all the top intersection numbers of divisors on the total space of the Poincare bundle restricted to the product of a curve and the abelian variety. We use these computations to find the class of the universal theta divisor and…

We determine the maximal dimension of compact subvarieties of $\mathcal{A}_g$, the moduli space of complex principally polarized abelian varieties of dimension $g$, and the maximal dimension of a compact subvariety through a very general…

In this paper we compute the pullback of divisor classes under the Prym map (extended to the boundary), and apply this result to get a lower bound on the slope of effective divisors on the perfect cone compactification of the moduli space…

We construct a compactification of the moduli spaces of abelian differentials on Riemann surfaces with prescribed zeroes and poles. This compactification, called the moduli space of multi-scale differentials, is a complex orbifold with…

In this paper we consider ideal sheaves associated to the singular loci of a divisor in a linear system $|L|$ of an ample line bundle on a complex abelian variety. We prove an effective result on their (continuous) global generation, after…

Starting from a beautiful idea of Kanev, we construct a uniformization of the moduli space A_6 of principally polarized abelian 6-folds in terms of curves and monodromy data. We show that the general ppav of dimension 6 is a Prym-Tyurin…

We study the cone of moving divisors on the moduli space ${\mathcal A}_g$ of principally polarized abelian varieties. Partly motivated by the generalized Rankin-Cohen bracket, we construct a non-linear holomorphic differential operator that…

We study the geometry of some varieties of sums of powers related to the Klein quartic. This allows us to describe the birational geometry of certain moduli spaces of abelian surfaces. In particular we show that the moduli space…

In this article we will construct a universal moduli space of stable parabolic vector bundles over the moduli space of marked Deligne-Mumford stable curves $\overline{M}_{_{g, n}}$. The objects that appear over the boundary of…

We study the rationality properties of the moduli space $\mathcal{A}_g$ of principally polarised abelian $g$-folds over $\mathbb{Q}$ and apply the results to arithmetic questions. In particular we show that any principally polarised abelian…

A uniform bound of intersection multiplicities of curves and divisors on abelian varieties is proved by algebraic geometric methods. It extends and improves a result obtained by A. Buium with a different method based on Kolchin's…

The moduli space of principally polarized abelian varieties with real structure and with level $N=4m$ structure (with $m \ge 1$) is shown to coincide with the set of real points of a quasi-projective algebraic variety defined over $\mathbb…

Let SU_X(3) be the moduli space of semi-stable vector bundles of rank 3 and trivial determinant on a curve X of genus 2. It maps onto P^8 and the map is a double cover branched over a sextic hypersurface called the Coble sextic. In the dual…

We describe the closure of the strata of abelian differentials with prescribed type of zeros and poles, in the projectivized Hodge bundle over the Deligne-Mumford moduli space of stable curves with marked points. We provide an explicit…

This is a survey paper on moduli spaces that have a natural structure of a (possibly incomplete) locally symmetric variety. We outline the Baily-Borel compactification for such varieties and compare it with the compactifications furnished…

The Weddle surface is classically known to be a birational (partially desingularized) model of the Kummer surface. In this note we go through its relations with moduli spaces of abelian varieties and of rank two vector bundles on a genus 2…

We construct spaces of coinvariants at principally polarized abelian varieties with respect to the action of an infinite-dimensional Lie algebra. We show how these spaces globalize to twisted $\mathcal{D}$-modules on moduli of principally…

Compactifications of moduli spaces of (1,p)-polarized abelian surfaces with level structures of canonical type have been described in great detail by Hulek, Kahn and Weintraub. The aim of this paper is to determine some invariants of smooth…

For $4 \nmid L$ and $g$ large, we calculate the integral Picard groups of the moduli spaces of curves and principally polarized abelian varieties with level $L$ structures. In particular, we determine the divisibility properties of the…