Hodge Theory and Complex Algebraic Geometry II: Volume 2
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Hodge Theory and Complex Algebraic Geometry II: Volume 2 by Claire Voisin
Book DescriptionThe 2003 second volume of this account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard-Lefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray spectral sequence and the global invariant cycles follow. The main results of the second part are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly Nori's connectivity theorem, which generalizes the above. The last part of the book is devoted to the relationships between Hodge theory and algebraic cycles. The book concludes with the example of cycles on abelian varieties, where some results of Bloch and Beauville, for example, are expounded. The text is complemented by exercises giving useful results in complex algebraic geometry. It will be welcomed by researchers in both algebraic and differential geometry.
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Book DetailsISBN: 9780521802833
(228mm x 152mm x 24mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 3-Jul-2003
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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