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Graduate Texts in Mathematics

Combinatorial Convexity and Algebraic Geometry

Authors: Ewald, Guenter

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About this Textbook

The aim of this book is to provide an introduction for students and nonspecialists to a fascinating relation between combinatorial geometry and algebraic geometry, as it has developed during the last two decades. This relation is known as the theory of toric varieties or sometimes as torus embeddings. Chapters I-IV provide a self-contained introduction to the theory of convex poly­ topes and polyhedral sets and can be used independently of any applications to algebraic geometry. Chapter V forms a link between the first and second part of the book. Though its material belongs to combinatorial convexity, its definitions and theorems are motivated by toric varieties. Often they simply translate algebraic geometric facts into combinatorial language. Chapters VI-VIII introduce toric va­ rieties in an elementary way, but one which may not, for specialists, be the most elegant. In considering toric varieties, many of the general notions of algebraic geometry occur and they can be dealt with in a concrete way. Therefore, Part 2 of the book may also serve as an introduction to algebraic geometry and preparation for farther reaching texts about this field. The prerequisites for both parts of the book are standard facts in linear algebra (including some facts on rings and fields) and calculus. Assuming those, all proofs in Chapters I-VII are complete with one exception (IV, Theorem 5.1). In Chapter VIII we use a few additional prerequisites with references from appropriate texts.

Reviews

"... an excellent addition to the literature of this fascinating research field." J. of Computational and Applied Mathematics / Newsletter on Computational and Applied Mathematics

G. Ewald

Combinatorial Convexity and Algebraic Geometry

"An excellent addition to the literature of this fascinating research field."—JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

"For anyone wishing to discover the connections between polytopes and algebraic geometry, this readable and well-organized text can be recommended."—MATHEMATICAL REVIEWS


Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-1-4612-4044-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA in USD
  • ISBN 978-0-387-94755-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA in USD
  • ISBN 978-1-4612-8476-5
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Combinatorial Convexity and Algebraic Geometry
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
168
Copyright
1996
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York, Inc.
eBook ISBN
978-1-4612-4044-0
DOI
10.1007/978-1-4612-4044-0
Hardcover ISBN
978-0-387-94755-6
Softcover ISBN
978-1-4612-8476-5
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XIV, 374
Topics

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