Hodge Theory and Complex Algebraic Geometry II
Hodge Theory and Complex Algebraic Geometry II
Volume 2:
February 2008
2
Available
Paperback
9780521718028
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
- 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
Product details
February 2008Paperback
9780521718028
362 pages
227 × 154 × 19 mm
0.57kg
4 b/w illus. 22 exercises
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.
