Rank Two Bundles on the Blow-up ofC2 Original Research Article

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 image(j) circled plus image(−j) for some integerj. We denote by imagejthe moduli space of holomorphic bundles on the blow-up ofC2whose restriction to the exceptional divisor is image(j) circled plus image(−j). We prove that imagejis generically a complex projective space of dimension 2j − 3.