Hodge Theory and Complex Algebraic Geometry II
Volume 2
$65.99 (P)
Part of Cambridge Studies in Advanced Mathematics
- Author: Claire Voisin, Institut des Hautes Études Scientifiques, Paris
- Translator: Leila Schneps
- Date Published: February 2008
- availability: Available
- format: Paperback
- isbn: 9780521718028
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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
Read more- Suitable for researchers, advanced graduate students and academic researchers
- A modern treatment of the subject, now in paperback
- Exercises complement the main text, and give useful extra results
Reviews & endorsements
"Mathematical rewards [await] those who invest their mathematical energies in this beautiful pair of volumes." Bulletin of the AMS
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×Product details
- Date Published: February 2008
- format: Paperback
- isbn: 9780521718028
- length: 362 pages
- dimensions: 227 x 154 x 19 mm
- weight: 0.57kg
- contains: 4 b/w illus. 22 exercises
- availability: Available
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.
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