Hodge Theory and Complex Algebraic Geometry I, Volume 1

Hodge Theory and Complex Algebraic Geometry I, Volume 1

by Claire Voisin
     
 

ISBN-10: 0521718015

ISBN-13: 9780521718011

Pub. Date: 02/28/2008

Publisher: Cambridge University Press

This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler

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Overview

This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.

Product Details

ISBN-13:
9780521718011
Publisher:
Cambridge University Press
Publication date:
02/28/2008
Series:
Cambridge Studies in Advanced Mathematics Series, #76
Edition description:
New Edition
Pages:
334
Product dimensions:
5.98(w) x 8.98(h) x 0.75(d)

Related Subjects

Table of Contents

Introduction1
IPreliminaries19
1Holomorphic Functions of Many Variables21
2Complex Manifolds38
3Kahler Metrics63
4Sheaves and Cohomology83
IIThe Hodge Decomposition115
5Harmonic Forms and Cohomology117
6The Case of Kahler Manifolds137
7Hodge Structures and Polarisations156
8Holomorphic de Rham Complexes and Spectral Sequences184
IIIVariations of Hodge Structure217
9Families and Deformations219
10Variations of Hodge Structure239
IVCycles and Cycle Classes261
11Hodge Classes263
12Deligne-Beilinson Cohomology and the Abel-Jacobi Map290
Bibliography315
Index319

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