Lecture Notes in Mathematics

By: Vasile Brinzanescu

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Paperback | 18 April 1996

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188 Pages

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24.13 x 15.88 x 1.27

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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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You Can Find This Book In

Non-Fiction Mathematics Algebra Calculus & Mathematical Analysis Complex Analysis Geometry Differential & Riemannian Geometry Algebraic Geometry Topology Algebraic Topology Analytic Geometry

Vector bundles over complex manifolds	p. 1
Vector bundles	p. 1
Chern classes	p. 7
GAGA Theorems	p. 14
Torsion-free and reflexive coherent sheaves	p. 16
Problems on vector bundles	p. 23
Facts on compact complex surfaces	p. 29
Line bundles and divisors	p. 29
Algebraic dimension and Kodaira dimension	p. 34
Classification and examples of surfaces	p. 39
Intersection form and Neron-Severi group	p. 49
Line bundles over surfaces	p. 53
Holomorphic structures in line bundles	p. 53
Picard group for tori	p. 57
Neron-Severi group for some elliptic surfaces	p. 61
Picard group for primary Kodaira surfaces	p. 70
Existence of holomorphic vector bundles	p. 85
Serre construction	p. 85
Filtrable vector bundles	p. 91
Non-filtrable and irreducible vector bundles	p. 104
Simple filtrable vector bundles	p. 110
Classification of vector bundles	p. 119
Deformations of vector bundles and applications	p. 119
Moduli spaces of simple vector bundles	p. 128
Stable vector bundles	p. 133
Moduli spaces of stable vector bundles	p. 143
Vector bundles over ruled surfaces	p. 148
References	p. 157
Index	p. 167
Table of Contents provided by Blackwell. All Rights Reserved.

Lecture Notes in Mathematics

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Paperback

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