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Geometry of Toric Varieties
Edited by: Laurent Bonavero and Michel Brion, Institut Fourier, Saint-Martin d'Hères, France
A publication of the Société Mathématique de France.
Séminaires et Congrès
2002; 272 pp; softcover
Number: 6
ISBN-10: 2-85629-122-8
ISBN-13: 978-2-85629-122-1
List Price: US$78
Individual Members: US$70.20
Institutional Members: US$62.40
Order Code: SECO/6
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Toric varieties form a beautiful class of algebraic varieties, which are often used as a testing ground for verifying general conjectures in algebraic geometry, for example, in Hilbert schemes, singularity theory, Mori theory, and so on.

This volume gathers expanded versions of lectures presented during the summer school of "Geometry of Toric Varieties" in Grenoble (France). These lectures were given during the second and third weeks of the school. (The first week was devoted to introductory material.) The paper by D. Cox is an overview of recent work in toric varieties and its applications, putting the other contributions of the volume into perspective.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.


Graduate students and research mathematicians interested in algebra and algebraic geometry.

Table of Contents

  • D. A. Cox -- Update on toric geometry
  • W. Bruns and J. Gubeladze -- Semigroup algebras and discrete geometry
  • A. Craw and M. Reid -- How to calculate A-Hilb \(\mathbb{C}^3\)
  • D. I. Dais -- Resolving 3-dimensional toric singularities
  • D. I. Dais -- Crepant resolutions of Gorenstein toric singularities and upper bound theorem
  • J. Hausen -- Producing good quotients by embedding into toric varieties
  • Y. Ito -- Special McKay correspondence
  • Y. Tschinkel -- Lectures on height zeta functions of toric varieties
  • J. A. Wiśniewski -- Toric Mori theory and Fano manifolds
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