Holomorphic bundles on O(− k) are algebraic

Abstract

We show that holomorphic bundles on O(−k) for k>0 are algebraic. We also show that holomorphic bundles on O(−1) are trivial outside the zero section. A corollary is that bundles on the blow-up of a surface at a point are trivial on a neighborhood of the exceptional divisor minus the exceptional divisor.