Holomorphic Vector Bundles over Compact Complex Surfaces

Vasile Brînzănescu (auth.)3540610189, 9783540610182

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.

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Table of contents :
Vector bundles over complex manifolds….Pages 1-27
Facts on compact complex surfaces….Pages 29-52
Line bundles over surfaces….Pages 53-83
Existence of holomorphic vector bundles….Pages 85-117
Classification of vector bundles….Pages 119-155