Hodge Theory and Complex Algebraic Geometry I:, Volume 1

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Cambridge University Press, Dec 20, 2007 - Mathematics - 334 pages
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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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About the author (2007)

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

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