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

Abstract

Let $f_s:X_s\to {\mathbf{P}}^2$ 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 ${\mathbf{P}}^2$.

6 pages, no figures