Rank-2 ample vector bundles on some smooth rational surfaces

Abstract

Some classification results for ample vector bundles of rank 2 on Hirzebruch surfaces, and on Del Pezzo surfaces, are obtained. In particular, we classify rank-2 ample vector bundles with $c_2$ less than 7 on Hirzebruch surfaces, and with $c_2$ less than 4 on Del Pezzo surfaces.

AMS-TeX v2.1, 29 pages