Hodge Theory and Complex Algebraic Geometry I: Volume 1
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Hodge Theory and Complex Algebraic Geometry I: Volume 1 by Claire Voisin
Book DescriptionThe 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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Book DetailsISBN: 9780521802604
(228mm x 152mm x 22mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 5-Dec-2002
Country of Publication: United Kingdom
Books By Author Claire Voisin
Chow Rings, Decomposition of the Diagonal, and the Topology of Families, Paperback (March 2014)
Provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. This title delves into arguments originating in Nori's work that have been further developed by others.
Hodge Theory and Complex Algebraic Geometry I: Volume 1, Paperback (December 2007)
The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure written for students.
Hodge Theory and Complex Algebraic Geometry II: Volume 2, Paperback (December 2007)» View all books by Claire Voisin
The second of two volumes offering a modern account of Kaehlerian geometry and Hodge theory for researchers in algebraic and differential geometry.
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Author Biography - Claire Voisin
Claire Voisin is a Professor at the Institut des Hautes Etudes Scientifiques, France
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