Globally generated vector bundles on the Segre threefold with Picard number two

Abstract

We classify globally generated vector bundles on ${\mathbb{P}}^1\times {\mathbb{P}}^2$ with small first Chern class, i.e. $c_1=(a,b)$, $a+b\le 3$. Our main method is to investigate the associated smooth curves to globally generated vector bundles via the Hartshorne-Serre construction.

21 pages; Comments welcome

References in corpus (1)

• Globally Generated Vector Bundles on P^n with c_1=3

Cited by in corpus (1)

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