Parabolic ample bundles

Abstract

We construct projectivization of a parabolic vector bundle and a tautological line bundle over it. It is shown that a parabolic vector bundle is ample if and only if the tautological line bundle is ample. This allows us to generalize the notion of a k-ample bundle, introduced by Sommese, to the context of parabolic bundles. A parabolic vector bundle E∗ is defined to be k-ample if the tautological line bundle OP(E∗)(1) is k-ample. We establish some properties of parabolic k-ample bundles.