Varieties with generically nef tangent bundles

Abstract

We study the geometry of projective manifolds whose tangent bundles are nef on sufficiently general curves (i.e. the tangent bundle is generically nef) and show that manifolds whose anticanonical bundles are semi-ample have this property. Furthermore we introduce a notion of sufficient nefness and investigate the relation with manifolds whose anticanonical bundles are nef.