Seshadri constants of parabolic vector bundles

Abstract

Let $X$ be a complex projective variety, and let $E_{\ast}$ be a parabolic vector bundle on $X$. We introduce the notion of \textit{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 parabolic Seshadri constants. We also compute parabolic Seshadri constants for symmetric powers and tensor products of parabolic vector bundles.