Stability of syzygy bundles on smooth projective varieties

TL;DR

This paper proves that syzygy bundles associated with sufficiently ample line bundles on smooth projective varieties are slope stable under any polarization, confirming a conjecture by Ein-Lazarsfeld-Mustopa.

Contribution

It establishes the slope stability of syzygy bundles on smooth projective varieties for ample line bundles, settling a previously conjectured property.

Findings

Syzygy bundles are slope stable with respect to any polarization.

The result applies to sufficiently ample line bundles.

It confirms a conjecture by Ein-Lazarsfeld-Mustopa.

Abstract

We prove that the kernel bundle of the evaluation morphism of global sections, namely the syzygy bundle, of a sufficiently ample line bundle on a smooth projective variety is slope stable with respect to any polarization. This settles a conjecture of Ein-Lazarsfeld-Mustopa.