Cohomology of vector bundles from a double cover of the projective plane

Abstract

The paper deals with locally free sheaves $\mathcal{F}_{p,q}$ on $\mathbb{P}^{2}$ obtained from a morphism $\mathbb{P}^{1}\times\mathbb{P}^{1}\to\mathbb{P}^{2}$. Bases of $\mathrm{H}^{i}(\mathbb{P}^{2},\mathcal{F}_{p,q})$ are explicitly given in terms of elements of certain local cohomology modules, which built up canonically a complex for computing cohomology modules of locally free sheaves on $\mathbb{P}^{2}$.