Holomorphic and algebraic vector bundles on 0-convex algebraic surfaces

Abstract

LetX be a smooth complex algebraic surface such that there is a proper birational morphism/:X → Y withY an affine variety. Let Xhol be the 2-dimensional complex manifold associated toX. Here we give conditions onX which imply that every holomorphic vector bundle onX is algebraizable and it is an extension of line bundles. We also give an approximation theorem of holomorphic vector bundles on Xhol (X normal algebraic surface) by algebraic vector bundles.