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

Edoardo Ballico, Sukmoon Huh, Francesco Malaspina

Published 2012-11-12, updated 2012-12-13Version 2

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.