ENGLISH

Combinatorial Convexity and Algebraic Geometry

By Günter Ewald

Book information

Publisher
Springer
Year
1996
ISBN
9780387947556, 0-387-94755-8, 0-387-94755-8
LCC
QA639.5 .E93 1996
Open Library ID
OL974797M
Language
english
Format
PDF
Filesize
11 MB (11963150 bytes)
Series
Graduate Texts in Mathematics
Edition
1
Pages
195\195
Library
Springer
Time added
2009-08-06 07:02:15

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.

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