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25 Remote Warehouse Mathematics- Algebraic Geometry

Cambridge Studies in Advanced Mathematics #76: Hodge Theory and Complex Algebraic Geometry I: Volume 1

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Cambridge Studies in Advanced Mathematics #76: Hodge Theory and Complex Algebraic Geometry I: Volume 1 Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure written for students.

About the Author

Claire Voisin is a Professor at the Institut des Hautes Études Scientifiques, France

Table of Contents

Introduction; Part I. Preliminaries: 1. Holomorphic functions of many variables; 2. Complex manifolds; 3. Kähler metrics; 4. Sheaves and cohomology; Part II. The Hodge Decomposition: 5. Harmonic forms and cohomology; 6. The case of Kähler manifolds; 7. Hodge structures and polarisations; 8. Holomorphic de Rham complexes and spectral sequences; Part III. Variations of Hodge Structure: 9. Families and deformations; 10. Variations of Hodge structure; Part IV. Cycles and Cycle Classes: 11. Hodge classes; 12. Deligne-Beilinson cohomology and the Abel-Jacobi map; Bibliography; Index.

Product Details

ISBN:
9780521718011
Author:
Voisin, Claire
Publisher:
Cambridge University Press
Translator:
Schneps, Leila
Author:
Schneps, Leila
Location:
Cambridge
Subject:
Geometry - Algebraic
Subject:
General
Subject:
Applied
Subject:
Mathematics-Algebraic Geometry
Subject:
Topology
Edition Description:
Trade paper
Series:
Cambridge Studies in Advanced Mathematics
Series Volume:
76
Publication Date:
20080231
Binding:
TRADE PAPER
Language:
English
Illustrations:
30 exercises
Pages:
334
Dimensions:
8.94x6.02x.69 in. 1.17 lbs.

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Cambridge Studies in Advanced Mathematics #76: Hodge Theory and Complex Algebraic Geometry I: Volume 1 New Trade Paper
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Product details 334 pages Cambridge University Press - English 9780521718011 Reviews:
"Synopsis" by , The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure written for students.
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