Hodge Theory and Complex Algebraic Geometry I: Volume 1

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Cambridge University Press, Dec 5, 2002 - Mathematics
The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.
 

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Contents

Part II The Hodge Decomposition
115
Part III Variations of Hodge Structure
217
Part IV Cycles and Cycle Classes
261

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About the author (2002)

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

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