Combinatorial Convexity and Algebraic Geometry

Description

This text provides an introduction to the theory of convex polytopes and polyhedral sets, to algebraic geometry and to the fascinating connections between these fields: the theory of toric varieties (or torus embeddings). The fist part of the book contains an introduction to the theory of polytopes - one of the most important parts of classical geometry in n-dimensional Euclidean space. Since the discussion here is independent of any applications to algebraic geometry, it would also be suitable for a course in geometry. This part also provides large parts of the mathematical background of linear optimization and of the geometrical aspects in Computer Science. The second part introduces toric varieties in an elementary way, building on the concepts of combinatorial geometry introduced in the first part. Many of the general concepts of algebraic geometry arise in this treatment and can be dealt with concretely. This part of the book can thus serve for a one-semester introduction to algebraic geometry, with the first part serving as a reference for combinatorial geometry.

Subjects

Other Editions

• Combinatorial Convexity and Algebraic GeometrypaperbackSpringer New York2011-09-17
• Combinatorial Convexity and Algebraic GeometryIsland Press1996
• Combinatorial Convexity and Algebraic GeometrySpringer London, Limited2012-01-01