Seshadri constants of parabolic vector bundles

TL;DR

This paper introduces parabolic Seshadri constants for parabolic vector bundles on complex projective varieties, establishing their properties, criteria for ampleness, and calculations for symmetric powers and tensor products.

Contribution

It defines and analyzes parabolic Seshadri constants, extending classical concepts to the parabolic setting with new criteria and computations.

Findings

Parabolic Seshadri constants are analogous to classical Seshadri constants.

A Seshadri criterion for parabolic ampleness is established.

Explicit computations for symmetric powers and tensor products are provided.

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.