On higher rank globally generated vector bundles over a smooth quadric   threefold
  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. 
Edoardo Ballico, Sukmoon Huh and Francesco Malaspina
math.AG