New trends in algebraic geometry : EuroConference on Algebraic Geometry, Warwick, July 1996 / edited by Klaus Hulek [and others].

Includes bibliographical references.

Print version record.

Birational Calabi -- Yau n-folds have equal Betti numbers / Victor V. Batyrev -- A Calabi -- Yau threefold with non-Abelian fundamental group / Arnaud Beauville -- Algebraic Gromov -- Witten invariants / K. Behrend -- Kahler hyperbolicity and variations of Hodge structures / Philippe Eyssidieux -- Algorithms for computing intersection numbers on moduli spaces of curves, with an application to the class of the locus of Jacobians / Carel Faber -- On some tensor representations of the Cremona group of the projective plane / Marat Gizatullin -- Hilbert schemes and simple singularities / Y. Ito and I. Nakamura -- Bounds for Seshadri constants / Oliver Kuchle and Andress Steffens -- Degenerate double covers of the projective plane / Marco Manetti -- The geometry underlying mirror symmetry / David R. Morrison -- Duality of polarized K3 surfaces / Shigeru Mukai -- On symplectic invariants of algebraic varieties coming from crepant contractions / Roberto Paoletti -- The Bogomolov -- Pantev resolution, an expository account / Kapil H. Paranjape -- Mordell-Weil lattices for higher genus fibration over a curve / Tetsuji Shioda -- Symplectic Gromov-Witten invariants / Bernd Siebert -- A generic Torelli theorem for the quintic threefold / Claire Voisin -- Flops, Type III contractions and Gromov-Witten invariants on Calabi-Yau threefolds / P. M. H. Wilson.

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.

English.

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