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Hodge theory and complex algebraic geometry 1

✍ Scribed by Claire Voisin, Leila Schneps

Book ID
127418426
Publisher
Cambridge University Press
Year
2003
Tongue
English
Weight
3 MB
Series
Cambridge Studies in Adv Math.76
Edition
1st
Category
Library
ISBN
0511063520

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✦ Synopsis

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.

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