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New Trends in Algebraic Geometry

New Trends in Algebraic Geometry

Part of London Mathematical Society Lecture Note Series

V. V. Batyrev, A. Beauville, K. Behrend, Philippe Eyssidieux, C. Faber, M. Gizatullin, Y. Ito, O. Küchle, M. Manetti, D. R. Morrison, S. Mukai, I. Nakamura, R. Paoletti, K. H. Paranjape, B. Siebert, T. Shioda, A. Steffens, C. Voisin, P. M. H. Wilson
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  • Date Published: May 1999
  • availability: Available
  • format: Paperback
  • isbn: 9780521646598


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About the Authors
  • This book is the outcome of the 1996 Warwick Algebraic Geometry EuroConference, containing 17 survey and research articles selected from the most outstanding contemporary research topics in algebraic geometry. Several of the articles are expository: among these a beautiful short exposition by Paranjape of the new and very simple approach to the resolution of singularities; a detailed essay by Ito and Nakamura on the ubiquitous A,D,E classification, centred around simple surface singularities; a discussion by Morrison of the new special Lagrangian approach to giving geometric foundations to mirror symmetry; and two deep, informative surveys by Siebert and Behrend on Gromow-Witten invariants treating them from the point of view of algebraic and symplectic geometry. The remaining articles cover a wide cross-section of the most significant research topics in algebraic geometry. This includes Gromow-Witten invariants, Hodge theory, Calabi-Yau 3-folds, mirror symmetry and classification of varieties.

    • Indispensable for researchers in this area
    • Authors are top names
    • Covers state of the art results
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    Product details

    • Date Published: May 1999
    • format: Paperback
    • isbn: 9780521646598
    • length: 496 pages
    • dimensions: 229 x 152 x 28 mm
    • weight: 0.72kg
    • availability: Available
  • Table of Contents

    1. On the Betti number of birationally isomorphic projective varieties with trivial canonical bundles V. V. Batyrev
    2. A Calabi–Yau threefold with non-abelian fundamental group A. Beauville
    3. Introduction to the theory of Gromov–Witten K. Behrend
    4. Kähler-hyperbolicity and variations of Hodge structures Philippe Eyssidieux
    5. Algorithms for computing intersections numbers on moduli spaces of curves, with an application to the class of the locus of Jacobians C. Faber
    6. On some tensor representations of the Cremona group of the projective plane M. Gizatullin
    7. Hilbert schemes and simple singularities Y. Ito
    8. Bounds for Seshadri constants O. Küchle
    9. Degenerate double covers of the projective plane M. Manetti
    10. The geometry underlying mirror symmetry D. R. Morrison
    11. Duality of polarized K3 surfaces S. Mukai
    12. Hilbert schemes and simple singularities I. Nakamura
    13. On symplectic invariants of algebraic varieties coming from crepant contractions R. Paoletti
    14. Bogomolov-Pantev resolution - an expository account K. H. Paranjape
    15. Symplectic Gromov–Witten invariants B. Siebert
    16. Mordell–Weil lattices for higher genus fibration over a curve T. Shioda
    17. Bounds for Seshadri constants A. Steffens
    18. A generic Torelli theorem for the quintic threefold C. Voisin
    19. Flops, Type III contractions and Gromov-Witten invariants on Calabi-Yau threefolds P. M. H. Wilson.

  • Editors

    K. Hulek, Universität Hannover, Germany

    M. Reid, University of Warwick

    C. Peters, Université de Grenoble

    F. Catanese, Georg-August-Universität, Göttingen, Germany


    V. V. Batyrev, A. Beauville, K. Behrend, Philippe Eyssidieux, C. Faber, M. Gizatullin, Y. Ito, O. Küchle, M. Manetti, D. R. Morrison, S. Mukai, I. Nakamura, R. Paoletti, K. H. Paranjape, B. Siebert, T. Shioda, A. Steffens, C. Voisin, P. M. H. Wilson

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