Nef vector bundles on a projective space with first Chern class 3 and second Chern class 8

TL;DR

This paper classifies nef vector bundles on a projective space with specific Chern classes by providing minimal resolutions using a full strong exceptional collection of line bundles.

Contribution

It introduces a method to explicitly describe such vector bundles via minimal resolutions, advancing the understanding of their structure.

Findings

Explicit minimal resolutions for the bundles are constructed.

The classification is achieved over an algebraically closed field of characteristic zero.

The approach utilizes a full strong exceptional collection of line bundles.

Abstract

We describe nef vector bundles on a projective space with first Chern class three and second Chern class eight over an algebraically closed field of characteristic zero by giving them a minimal resolution in terms of a full strong exceptional collection of line bundles.