Stability of syzygy bundles on an algebraic surface

TL;DR

This paper proves that for a smooth projective surface over an algebraically closed field, the syzygy bundle associated with a sufficiently positive very ample line bundle is slope-stable, contributing to the understanding of vector bundle stability.

Contribution

It establishes the slope-stability of syzygy bundles on algebraic surfaces for sufficiently positive line bundles, a new result in the context of algebraic geometry.

Findings

Syzygy bundle M_L is slope-stable on smooth projective surfaces.

Stability holds for any sufficiently positive very ample line bundle.

Provides conditions under which M_L maintains stability.

Abstract

Given a very ample line bundle L on a projective variety X, the syzygy bundle M_L associated to L is the kernel of the evaluation map on sections of L. Our main result is that if X is a smooth projective surface defined over an algebraically closed field, then M_L is slope-stable for any sufficiently positive L.