![]() ![]() 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. Many of the general concepts of algebraic geometry arise in this treatment and can be dealt with concretely. Convex Bodies and Algebraic Geometry: An Introduction to the Theory of Toric Varieties (Ergebnisse der Mathematik und ihrer Grenzgebiete. Such sets occur naturally, and have been analyzed independently, in convex. The central objects of study in this rapidly developing field are convex sets with algebraic structure. A primary focus lies on the mathematical. Convex algebraic geometry is an evolving subject area arising from a synthesis of ideas and techniques from optimization, convex geometry, and algebraic geometry. The second part introduces toric varieties in an elementary way, building on the concepts of combinatorial geometry introduced in the first part. Convex algebraic geometry is an emerging field at the interface of convex optimization and algebraic geometry. This part also provides large parts of the mathematical background of linear optimization and of the geometrical aspects in Computer Science. Chapters I-IV provide a self-contained introduction to the theory of. Since the discussion here is independent of any applications to algebraic geometry, it would also be suitable for a course in geometry. This relation is known as the theory of toric varieties or sometimes as 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. 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). Combinatorial geometry, Geometry, Algebraic, Toric varieties In algebraic geometry, convexity is a restrictive technical condition for algebraic varieties originally introduced to analyze Kontsevich moduli spaces in quantum cohomology. ![]()
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