Holomorphic Vector Bundles over Compact Complex Surfaces

✍ Scribed by Vasile Brînzănescu (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1996
• Tongue: English
• Leaves: 174
• Series: Lecture Notes in Mathematics 1624
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ 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

✦ Subjects

Differential Geometry; Algebraic Geometry; Algebraic Topology