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9780521646598

New Trends in Algebraic Geometry

by
  • ISBN13:

    9780521646598

  • ISBN10:

    0521646596

  • Format: Paperback
  • Copyright: 1999-05-28
  • Publisher: Cambridge University Press

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Supplemental Materials

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Summary

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.

Table of Contents

Birational Calabi--Yau n-folds have equal Betti numbers
1(13)
Victor V. Batyrev
A Calabi--Yau threefold with non-Abelian fundamental group
13(6)
Arnaud Beauville
Algebraic Gromov--Witten invariants
19(52)
K. Behrend
Kahler hyperbolicity and variations of Hodge structures
71(22)
Philippe Eyssidieux
Algorithms for computing intersection numbers on moduli spaces of curves, with an application to the class of the locus of Jacobians
93(18)
Carel Faber
On some tensor representations of the Cremona group of the projective plane
111(40)
Marat Gizatullin
Hilbert schemes and simple singularities
151(84)
Y. Ito
I. Nakamura
Bounds for Seshadri constants
235(20)
Oliver Kuchle
Andreas Steffens
Degenerate double covers of the projective plane
255(28)
Marco Manetti
The geometry underlying mirror symmetry
283(28)
David R. Morrison
Duality of polarized K3 surfaces
311(16)
Shigeru Mukai
On symplectic invariants of algebraic varieties coming from crepant contractions
327(20)
Roberto Paoletti
The Bogomolov--Pantev resolution, an expository account
347(12)
Kapil H. Paranjape
Mordell--Weil lattices for higher genus fibration over a curve
359(16)
Tetsuji Shioda
Symplectic Gromov--Witten invariants
375(50)
Bernd Siebert
A generic Torelli theorem for the quintic threefold
425(40)
Claire Voisin
Flops, Type III contractions and Gromov--Witten invariants on Calabi--Yau threefolds
465
P.M.H. Wilson

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