Stability of syzygy bundles on abelian varieties

TL;DR

This paper proves that the syzygy bundle associated with a sufficiently ample line bundle on an abelian variety is stable, confirming a conjecture in this context and advancing understanding of vector bundle stability on abelian varieties.

Contribution

It establishes the stability of syzygy bundles on abelian varieties, settling a conjecture by Ein-Lazarsfeld-Mustopa for this class of varieties.

Findings

Syzygy bundles are stable on abelian varieties with sufficiently ample line bundles.

Confirms a conjecture by Ein-Lazarsfeld-Mustopa in the case of abelian varieties.

Advances the theory of vector bundle stability in algebraic geometry.

Abstract

We prove that the kernel of the evaluation morphism of global sections - namely the syzygy bundle - of a sufficiently ample line bundle on an abelian variety is stable. This settles a conjecture of Ein-Lazarsfeld-Mustopa, in the case of abelian varieties.