Hodge Theory and Complex Algebraic Geometry II: Volume 2

by Claire Voisin, Leila Schneps

Overview

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

Product Details

ISBN-13:	9780521718028
Publisher:	Cambridge University Press
Publication date:	12/20/2007
Series:	Cambridge Studies in Advanced Mathematics , #77
Edition description:	New Edition
Pages:	362
Product dimensions:	6.06(w) x 8.94(h) x 0.75(d)

About the Author

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

Table of Contents

Introduction. Part I. The Topology of Algebraic Varieties: 1. The Lefschetz theorem on hyperplane sections; 2. Lefschetz pencils; 3. Monodromy; 4. The Leray spectral sequence; Part II. Variations of Hodge Structure: 5. Transversality and applications; 6. Hodge filtration of hypersurfaces; 7. Normal functions and infinitesimal invariants; 8. Nori's work; Part III. Algebraic Cycles: 9. Chow groups; 10. Mumford' theorem and its generalisations; 11. The Bloch conjecture and its generalisations; References; Index.

Editorial Reviews

"Mathematical rewards [await] those who invest their mathematical energies in this beautiful pair of volumes." Bulletin of the AMS

From the Publisher