Local positivity, multiplier ideals, and syzygies of abelian varieties

TL;DR

This paper explores the relationship between local positivity, multiplier ideals, and syzygies of abelian varieties, extending known results on projective normality to higher syzygies using multiplier ideals.

Contribution

It introduces a new approach linking local positivity and syzygies of abelian varieties via multiplier ideals, extending previous results to higher syzygies.

Findings

Established a connection between local positivity and syzygies using multiplier ideals.

Extended Hwang and To's results on projective normality to higher syzygies.

Provided a framework for analyzing syzygies of abelian varieties through local positivity.

Abstract

We use the language of multiplier ideals in order to relate the syzygies of an abelian variety in a suitable embedding with the local positivity of the line bundle inducing that embedding. This extends to higher syzygies a result of Hwang and To on projective normality.