Globally generated vector bundles on ${\mathbf{P}}^1\times {\mathbf{P}}^1\times {\mathbf{P}}^1$ with low first Chern classes

Abstract

We classify globally generated vector bundles on ${\mathbf{P}}^1\times {\mathbf{P}}^1\times {\mathbf{P}}^1$ with small first Chern class, i.e. $c_1=(a_1,a_2,a_3)$, $a_i\le 2$. Our main method is to investigate the associated smooth curves to globally generated vector bundles via the Hartshorne-Serre correspondence.

34 pages; Comments welcome

References in corpus (2)

• Globally Generated Vector Bundles on P^n with c_1=3
• Globally generated vector bundles on the Segre threefold with Picard number two