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Hodge Theory and Complex Algebraic Geometry II

Hodge Theory and Complex Algebraic Geometry II - 03 edition

ISBN13: 978-0521802833

Cover of Hodge Theory and Complex Algebraic Geometry II 03 (ISBN 978-0521802833)
ISBN13: 978-0521802833
ISBN10: 0521802830
Cover type: Hardback
Edition/Copyright: 03
Publisher: Cambridge University Press
Published: 2003
International: No

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Hodge Theory and Complex Algebraic Geometry II - 03 edition

ISBN13: 978-0521802833

Claire Voisin and Leila Schneps Trans.

ISBN13: 978-0521802833
ISBN10: 0521802830
Cover type: Hardback
Edition/Copyright: 03
Publisher: Cambridge University Press

Published: 2003
International: No
Summary

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.

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 generalizations
11. The Bloch conjecture and its generalizations
Bibliography
Index.

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