On higher rank globally generated vector bundles over a smooth quadric threefold

TL;DR

This paper classifies globally generated rank 3 vector bundles on smooth quadric threefolds with low first Chern class and extends the classification to higher ranks, also analyzing conditions for indecomposability.

Contribution

It provides a complete classification of such vector bundles for rank 3 and higher, including criteria for indecomposability, advancing understanding of vector bundles on quadrics.

Findings

Complete classification for rank 3 bundles with c_1 ≤ 2

Extension of classification to higher ranks

Conditions for indecomposability of vector bundles

Abstract

We give a complete classification of globally generated vector bundles of rank 3 on a smooth quadric threefold with $c_1\leq 2$ and extend the result to arbitrary higher rank case. We also investigate the existence of globally generated indecomposable vector bundles, and give the sufficient and necessary conditions on numeric data of vector bundles for indecomposability.