Stability conditions for restrictions of vector bundles on projective surfaces

TL;DR

This paper establishes criteria using Bridgeland stability conditions to determine when stable vector bundles on surfaces remain stable upon restriction to curves, with applications to cohomology computations on specific surfaces.

Contribution

It introduces new stability criteria for restricting vector bundles on surfaces and provides explicit cohomology calculations for bundles on planes and Hirzebruch surfaces.

Findings

Criteria for stability preservation upon restriction

Stronger conditions for general bundles on the plane

Cohomology computations for bundles on specific surfaces

Abstract

Using Bridgeland stability conditions we give sufficient criteria for a stable vector bundle on a surface to remain stable when restricted to a curve. We give a stronger criterion when the vector bundle is a general vector bundle on the plane. As an application, we compute the cohomology of such bundles for curves that lie in the plane or on Hirzebruch surfaces.