A criterion for an abelian variety to be non-simple

TL;DR

This paper provides a criterion based on period matrices to determine when a polarized abelian variety is non-simple, with multiple examples illustrating the criterion.

Contribution

It introduces a new criterion involving period matrices to identify non-simple polarized abelian varieties, expanding tools for their analysis.

Findings

Criterion effectively distinguishes non-simple abelian varieties

Several explicit examples demonstrate the criterion's application

Enhances understanding of the structure of polarized abelian varieties

Abstract

We give a criterion in terms of period matrices for an arbitrary polarized abelian variety to be non-simple. Several examples are worked out.