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What is a toric variety? (English) Zbl 1038.14021
Goldman, Ron (ed.) et al., Topics in algebraic geometry and geometric modeling. Proceedings of the workshop on algebraic geometry and geometric modeling, July 29–August 2, 2002, Vilnius, Lithuania. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3420-7/pbk). Contemp. Math. 334, 203-223 (2003).
From the introduction: This article is an introduction to toric varieties for non-specialists. It discusses their definition using fans, homogeneous coordinates, and polytopes. Many examples are given to illustrate the various definitions. The paper is organized into 14 sections as follows: Varieties, toric varieties, examples of toric varieties, cones, affine toric varieties, coordinate rings, normality, fans and toric varieties, properties of toric varieties, homogeneous coordinates, examples of homogeneous coordinates, the toric variety of a polytope, polytopes and homogeneous coordinates, and bibliography. The bibilography contains 25 items in 5 categories: Basic references on toric varieties, basic references on algebraic geometry, basic references on cones and polytopes, introductory articles on toric varieties and other articles on toric varieties.
For the entire collection see [Zbl 1029.00024].

14M25 Toric varieties, Newton polyhedra, Okounkov bodies