Characterization of products of theta divisors

Abstract

We study products of irreducible theta divisors from two points of view. Onthe one hand, we characterize them as normal subvarieties of abelian varieties such that adesingularization has holomorphic Euler characteristic 1. On the other hand, we identify themup to birational equivalence among all varieties of maximal Albanese dimension. We alsodescribe the structure of varieties $X$ of maximal Albanese dimension, with holomorphic Eulercharacteristic 1 and irregularity 2 dim $X−1$.