A splitting criterion for vector bundles on blowing ups of the plane

Edoardo Ballico; Francesco Malaspina

A splitting criterion for vector bundles on blowing ups of the plane

Algebraic Geometry 2008-04-02 v1

Authors: Edoardo Ballico , Francesco Malaspina

Abstract

Let $f_s: X_s \to {\bf {P}}^2$ be the blowing-up of $s$ distinct points and $E$ a vector bundle on $X_s$ . Here we give a cohomological criterio which is equivalent to $E \cong f_s^\ast (A)$ with $A$ a direct sum of line bundles. We also some cohomological characterizations of very particular rank 2 vector bundles on ${\bf {P}}^2$ .

Keywords

vector bundles blowing ups splitting criterion cohomological characterization line bundles rank 2 vector bundles projective plane

Cite

@article{arxiv.0804.0098,
  title  = {A splitting criterion for vector bundles on blowing ups of the plane},
  author = {Edoardo Ballico and Francesco Malaspina},
  journal= {arXiv preprint arXiv:0804.0098},
  year   = {2008}
}

Comments

6 pages, no figures

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