Rank Two Bundles on the Blow-up ofC2

Abstract

In this paper we study holomorphic rank two vector bundles on the blow-up ofC2with vanishing Chern class. The restriction of such a bundle over the exceptional divisor splits as O(j)⊕O(−j) for some integerj. We denote by Mjthe moduli space of holomorphic bundles on the blow-up ofC2whose restriction to the exceptional divisor is O(j)⊕O(−j). We prove that Mjis generically a complex projective space of dimension 2j−3.