Pullback and Direct Image of Parabolic Ample and Parabolic Nef Vector Bundles

TL;DR

This paper establishes that the pullback and direct image operations preserve parabolic ampleness and nefness of vector bundles under finite surjective maps between smooth complex projective curves, characterizing when these properties are maintained.

Contribution

It provides a precise criterion for when pullback and direct image of parabolic vector bundles preserve ampleness and nefness on smooth complex projective curves.

Findings

Pullback of parabolic ample bundles remains ample.

Direct image of parabolic nef bundles remains nef.

Characterization of when these properties are preserved.

Abstract

We prove that under a finite surjective map of irreducible smooth complex projective curves, the pullback and direct image of a parabolic ample (respectively, parabolic nef) vector bundle is again parabolic ample (respectively, parabolic nef) if and only if the original parabolic vector bundle is parabolic ample (respectively, parabolic nef).