Parabolic k-ample bundles

TL;DR

This paper generalizes the concept of k-ample bundles to parabolic vector bundles by constructing their projectivization and tautological line bundles, establishing criteria for ampleness, and exploring properties of these generalized bundles.

Contribution

It introduces the notion of parabolic k-ample bundles, extending Sommese's k-ample concept to the parabolic setting with new construction and characterization methods.

Findings

A parabolic vector bundle is ample iff its tautological line bundle is ample.

Defined parabolic k-ample bundles via tautological line bundle properties.

Established properties and criteria for parabolic k-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 ${\mathcal O}_{{\mathbb P}(E_*)}(1)$ is $k$--ample. We establish some properties of parabolic k-ample bundles.