# The basepoint-freeness threshold and syzygies of abelian varieties

## TL;DR

This paper demonstrates how a specific constant related to polarized abelian varieties reveals information about their syzygies, providing a new proof of Lazarsfeld's conjecture that is characteristic-free.

## Contribution

It introduces a natural constant that encodes syzygy information and offers a characteristic-free proof of Lazarsfeld's conjecture on abelian varieties.

## Key findings

- The constant encodes syzygy information of the section ring.
- Provides a characteristic-free proof of Lazarsfeld's conjecture.
- Simplifies understanding of syzygies in polarized abelian varieties.

## Abstract

We show how a natural constant introduced by Jiang and Pareschi for a polarized abelian variety encodes information about the syzygies of the section ring of the polarization. As a particular case this gives a quick and characteristic-free proof of Lazarsfeld's conjecture on syzygies of abelian varieties, originally proved by Pareschi in characteristic zero.