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Hodge Theory and Complex Algebraic Geometry I

ISBN-10: 0521718015
ISBN-13: 9780521718011
Edition: 2007
List price: $62.00 Buy it from $60.21
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Description: 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  More...

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Book details

List price: $62.00
Copyright year: 2007
Publisher: Cambridge University Press
Publication date: 12/20/2007
Binding: Paperback
Pages: 334
Size: 6.00" wide x 8.75" long x 0.75" tall
Weight: 1.144
Language: English

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.

Claire Voisin has been a senior researcher at France's National Center for Scientific Research since 1986.

Introduction
Preliminaries
Holomorphic functions of many variables
Complex manifolds
K+�hler metrics
Sheaves and cohomology
The Hodge Decomposition
Harmonic forms and cohomology
The case of K+�hler manifolds
Hodge structures and polarisations
Holomorphic de Rham complexes
Variations of Hodge Structure
Families and deformations
Variations of Hodge structure
Cycles and Cycle Classes
Hodge classes
The AbelG++Jacobi map
Bibliography
Index

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