Toric varieties

Abstract

The study of toric varieties is a wonderful part of algebraic geometry. There are elegant theorems and deep connections with polytopes, polyhedra, combinatorics, commutative algebra, symplectic geometry, and topology. Toric varieties also have unexpected applications in areas as diverse as physics, coding theory, algebraic statistics, and geometric modeling. Moreover, as noted by Fulton [105], “toric varieties have provided a remarkably fertile testing ground for general theories.” At the same time, the concreteness of toric varieties provides an excellent context for someone encountering the powerful techniques of modern algebraic geometry for the first time. Our book is an introduction to this rich subject that assumes only a modest background yet leads to the frontier of this active area of research.