Séminaires et Congrès 2002; 272 pp; softcover Number: 6 ISBN10: 2856291228 ISBN13: 9782856291221 List Price: US$78 Individual Members: US$70.20 Institutional Members: US$62.40 Order Code: SECO/6
 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. Readership 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 AHilb \(\mathbb{C}^3\)
 D. I. Dais  Resolving 3dimensional 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
