A criterion for an abelian variety to be simple

TL;DR

This paper introduces a numerical criterion for determining when an abelian variety is simple, linking it to an invariant related to the s-invariant, with implications for the geometry of the ample cone.

Contribution

It provides a novel numerical criterion for simplicity of abelian varieties using a related invariant to the s-invariant, offering new examples and geometric insights.

Findings

New examples with irrational s-invariants

A criterion connecting simplicity to a geometric invariant

Insights into the ample cone's geometry

Abstract

In this note we give a numerical criterion that expresses the condition that an abelian variety be simple in terms of an invariant that is closely related to the s-invariant of Ein-Cutkosky-Lazarsfeld. The criterion yields new examples where s-invariants are irrational. It may also be viewed as a statement about the geometry of the ample cone.