Globally generated vector bundles of rank 2 on a smooth quadric threefold

TL;DR

This paper classifies rank 2 globally generated vector bundles with low first Chern class on a smooth quadric threefold, revealing that those with c1=3 are essentially odd instantons after twisting.

Contribution

It provides a complete classification of such vector bundles and establishes a link to odd instantons for c1=3.

Findings

Classification of rank 2 globally generated vector bundles with c1 ≤ 3

Identification of bundles with c1=3 as odd instantons up to twist

Determination of their Chern classes

Abstract

We investigate the existence of globally generated vector bundles of rank 2 with $c_1\leq 3$ on a smooth quadric threefold and determine their Chern classes. As an automatic consequence, every rank 2 globally generated vector bundle on $Q$ with $c_1=3$ is an odd instanton up to twist.