Characterization of products of theta divisors

TL;DR

This paper characterizes products of irreducible theta divisors as special subvarieties of abelian varieties with unique desingularization properties and classifies certain varieties with maximal Albanese dimension and specific Euler characteristic.

Contribution

It provides a new characterization of products of theta divisors and classifies maximal Albanese dimension varieties with Euler characteristic 1.

Findings

Products of theta divisors are normal subvarieties with unique Euler characteristic 1 desingularizations.

Identifies these products up to birational equivalence among varieties of maximal Albanese dimension.

Describes the structure of maximal Albanese dimension varieties with Euler characteristic 1 and irregularity 2dim X-1.

Abstract

We study products of irreducible theta divisors from two points of view. On the one hand, we characterize them as normal subvarieties of abelian varieties such that a desingularization has holomorphic Euler characteristic 1. On the other hand, we identify them up to birational equivalence among all varieties of maximal Albanese dimension. We also describe the structure of maximal Albanese dimension varieties X with holomorphic Euler characteristic 1 and irregularity 2dim X-1.