Holomorphic Vector Bundles over Compact Complex Surfaces (Lecture Notes in Mathematics (Springer-verlag), 1624.)

The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface. Special features of the nonalgebraic surfaces case, like irreducible vector bundles and stability with respect to a Gauduchon metric, are considered. The reader requires a grounding in geometry at graduate student level. The book will be of interest to graduate students and researchers in complex, algebraic and differential geometry. Vector bundles over complex manifolds.- Facts on compact complex surfaces.- Line bundles over surfaces.- Existence of holomorphic vector bundles.- Classification of vector bundles.