Hodge Theory and Complex Algebraic Geometry I

Name: Hodge Theory and Complex Algebraic Geometry I
Price: 50.14 USD
Availability: InStock
ISBN: 9780521718011

ISBN-10: 0521718015

ISBN-13: 9780521718011

Edition: 2007

Authors: Claire Voisin, Leila Schneps

List price: $64.99

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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 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.

Book details

List price: $64.99
Copyright year: 2007
Publisher: Cambridge University Press
Publication date: 12/20/2007
Binding: Paperback
Pages: 334
Size: 6.02" wide x 8.94" long x 0.71" tall
Weight: 1.144
Language: English

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+ï¿½hler metrics



Sheaves and cohomology



The Hodge Decomposition



Harmonic forms and cohomology



The case of K+ï¿½hler 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