Hodge theory and complex algebraic geometry. [EBook] / Claire Voisin ; translated by Leila Schneps. 2
Hodge theory and complex algebraic geometry. [EBook] / Claire Voisin ; translated by Leila Schneps. 2
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 PicardLefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray s...
Personal Name(s):  Voisin, Claire, (author) 

Schneps, Leila, (translator)  
Imprint: 
Cambridge :
Cambridge University Press,
2003

Physical Description: 
1 online resource (ix, 351 pages) 
Note: 
englisch 
ISBN: 
9780521718028 9780521802833 9780511615177 
Series Title: 
Cambridge studies in advanced mathematics ;
77 
Subject (LOC):  
Full Text 
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 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 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. 