Nef vector bundles on a projective space with first Chern class three

TL;DR

This paper classifies nef vector bundles on projective spaces with first Chern class three, revealing conditions for global generation based on the second Chern class and providing examples of nef bundles that are not globally generated.

Contribution

It provides a classification of nef vector bundles with specific Chern classes on projective spaces and identifies when they are globally generated.

Findings

Nef vector bundles are globally generated if second Chern class < 8.

Existence of nef but non-globally generated bundles with second Chern class 8 and 9.

Complete classification on projective spaces with first Chern class three.

Abstract

We classify nef vector bundles on a projective space with first Chern class three over an algebraically closed field of characteristic zero; we see, in particular, that these nef vector bundles are globally generated if the second Chern class is less than eight, and that there exist nef but non-globally generated vector bundles with second Chern class eight and nine on a projective plane.