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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ISBN-13
978-3-540-49845-2 (9783540498452)
DOI
Schweitzer Klassifikation
Vector bundles over complex manifolds.- Facts on compact complex surfaces.- Line bundles over surfaces.- Existence of holomorphic vector bundles.- Classification of vector bundles.
