Nef vector bundles on a projective space or a hyperquadric with the first Chern class small

TL;DR

This paper provides a new proof for classifying nef vector bundles on projective spaces and hyperquadrics with small first Chern class, refining previous results in algebraic geometry.

Contribution

It offers a novel proof of existing classification results for nef vector bundles with small first Chern class on specific algebraic varieties.

Findings

Classification of nef vector bundles with small first Chern class

New proof technique for existing theorems

Refinement of previous classification results

Abstract

We give a new proof of the classification due to Peternell-Szurek-Wi\'{s}niewski of nef vector bundles on a projective space with the first Chern class less than three and on a smooth hyperquadric with the first Chern class less than two over an algebraically closed field of characteristic zero.