Globally generated vector bundles on a smooth quadric surface

Abstract

We give the classification of globally generated vector bundles of rank $2$ on a smooth quadric surface with $c_1\le (2,2)$ in terms of the indices of the bundles, and extend the result to arbitrary higher rank case. We also investigate their indecomposability and give the sufficient and necessary condition on numeric data of vector bundles for indecomposability.

23 pages; Comments welcome; Several corrections

References in corpus (5)

• On globally generated vector bundles on projective spaces II
• Globally Generated Vector Bundles on P^n with c_1=3
• Globally Generated Vector Bundles on P^n with c_1=4
• Globally generated vector bundles of rank 2 on a smooth quadric threefold
• Rank two globally generated vector bundles with c_1 \leq 5