Stability conditions for restrictions of vector bundles on projective 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.

14 pages. Replaced with version to appear in Mich. Math. J