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Hodge Theory and Complex Algebraic Geometry II

Volume 2

$62.99 (P)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: February 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521718028

$ 62.99 (P)
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About the Authors
  • 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
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    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.

  • Author

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

    Translator

    Leila Schneps

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