Stability of Syzygy bundles corresponding to stable vector bundles on algebraic surfaces

TL;DR

This paper investigates the stability of syzygy bundles derived from stable, globally generated vector bundles on algebraic surfaces, focusing on how the stability property is preserved or affected.

Contribution

It provides new insights into the stability behavior of syzygy bundles associated with stable vector bundles on algebraic surfaces.

Findings

Stability conditions for syzygy bundles are established.

Criteria for stability preservation under certain conditions are identified.

Theoretical framework for analyzing syzygy bundle stability on surfaces is developed.

Abstract

Let $(X, H)$ be a polarized smooth projective algebraic surface and $E$ is globally generated, stable vector bundle on $X$. Then the Syzygy bundle $M_E$ associated to it is defined as the kernel bundle corresponding to the evaluation map. In this article we will study the stability property of $M_E$ with respect to $H$.