## Osaka Journal of Mathematics

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

I-Chiau Huang

#### 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 $\mathbb{P}^{2}$.

#### Article information

Source
Osaka J. Math., Volume 43, Number 3 (2006), 557-579.

Dates
First available in Project Euclid: 25 September 2006

https://projecteuclid.org/euclid.ojm/1159190001

Mathematical Reviews number (MathSciNet)
MR2283409

Zentralblatt MATH identifier
1107.14031

#### Citation

Huang, I-Chiau. Cohomology of vector bundles from a double cover of the projective plane. Osaka J. Math. 43 (2006), no. 3, 557--579. https://projecteuclid.org/euclid.ojm/1159190001