Seshadri constants of parabolic vector bundles

Abstract

Let $X$ be a complex projective variety, and let $E_{\ast }$ be a parabolic vector bundle on $X$ with parabolic structure on a divisor. We introduce the notion of parabolic Seshadri constants of $E_{\ast }$. It is shown that these constants are analogous to the classical Seshadri constants of vector bundles, in particular they have parallel definitions and properties. We prove a Seshadri criterion for parabolic ampleness of $E_{\ast }$ in terms of the parabolic Seshadri constants of it. We also compute parabolic Seshadri constants for symmetric powers and tensor products of parabolic vector bundles.