Hodge Theory and Complex Algebraic Geometry II: Volume 2 by C... - 9780521802833

Hodge Theory and Complex Algebraic Geometry II: Volume 2Author(s): Claire Voisin, Leila Schneps\nFormat: Hardback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9780521802833, 978-0521802833\nSynopsis\nThe 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 PicardLefschetz 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 NoetherLefschetz theorems, the generic triviality of the AbelJacobi 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 s.