(1) Department of Mathematics, University of Trento, 38050 Povo (TN), Italy;(2) Departamento de Matematica, Universidade Federal de Pernambuco Cidade Universitaria, 50670-901 Recife, PE, Brazil
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.