New Trends in Algebraic Geometry

Seventeen articles from the most outstanding contemporary topics in algebraic geometry.

K. Hulek (Edited by), M. Reid (Edited by), C. Peters (Edited by), F. Catanese (Edited by)

9780521646598, Cambridge University Press

Paperback, published 13 May 1999

496 pages
22.8 x 15.4 x 2.6 cm, 0.665 kg

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.

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.

Subject Areas: Algebraic geometry [PBMW]