Criteria for the ampleness of certain vector bundles

Abstract

We prove that certain vector bundles (of rank two over arbitrary manifolds or rank three over surfaces) are ample if they are so when restricted to divisors, certain numerical criteria hold, and they are semistable (with respect to det(E)). This result generalises a theorem of Schneider and Tancredi for rank two vector bundles over surfaces. We also provide counterexamples indicating that our theorem is sharp for rank three vector bundles over surfaces.