Stable vector bundles on projective surfaces

An effective variant of an arithmetic criterion for instability of vector bundles on a surface is considered. Namely, a lower bound is established for the degree of a destabilizing subsheaf in a vector bundle with positive discriminant. This bound, which depends on the rank and discriminant of the bundle, is used to prove that the restrictions of stable bundles on a surface to curves are stable, and to prove a number of other results.