New Trends in Algebraic Geometry

ISBN-13: 9780521646598 / Angielski / Miękka / 1999 / 496 str.

Klaus Hulek; M. Reid; K. Hulek

Opis

This book is the outcome of the 1996 Warwick Algebraic Geometry EuroConference, containing seventeen 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, centered 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

Spis treści

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.