Hodge Theory and Complex Algebraic Geometry II (Paperback)

Claire Voisin

ISBN 10: 0521718023 / ISBN 13: 9780521718028

Published by Cambridge University Press, Cambridge, 2008

About this Item

Paperback. The 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. The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. The main results 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 deals with the relationships between Hodge theory and algebraic cycles. The text is complemented by exercises offering useful results in complex algebraic geometry. Also available: Volume I 0-521-80260-1 Hardback $60.00 C Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9780521718028

Bibliographic Details

• Title: Hodge Theory and Complex Algebraic Geometry II (Paperback)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2008
• Language: English
• ISBN 10: 0521718023
• ISBN 13: 9780521718028
• Binding: Paperback
• Edition: 1st Edition
• Condition: new

About this title

Synopsis

The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. The main results 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 deals with the relationships between Hodge theory and algebraic cycles. The text is complemented by exercises offering useful results in complex algebraic geometry. Also available: Volume I 0-521-80260-1 Hardback $60.00 C

About the Author

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