Polytopes, Rings, and K-Theory

  • Authors
  • Joseph Gubeladze
  • Winfried Bruns

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-x
  2. Cones, monoids, and triangulations

    1. Front Matter
      Pages 1-1
    2. Winfried Bruns, Joseph Gubeladze
      Pages 3-48
    3. Winfried Bruns, Joseph Gubeladze
      Pages 49-89
    4. Winfried Bruns, Joseph Gubeladze
      Pages 91-119
  3. Affine monoid algebras

    1. Front Matter
      Pages 121-121
    2. Winfried Bruns, Joseph Gubeladze
      Pages 123-163
    3. Winfried Bruns, Joseph Gubeladze
      Pages 165-198
    4. Winfried Bruns, Joseph Gubeladze
      Pages 199-249
    5. Winfried Bruns, Joseph Gubeladze
      Pages 251-283
  4. K-theory

    1. Front Matter
      Pages 285-285
    2. Winfried Bruns, Joseph Gubeladze
      Pages 287-325
    3. Winfried Bruns, Joseph Gubeladze
      Pages 327-353
    4. Winfried Bruns, Joseph Gubeladze
      Pages 355-428
  5. Back Matter
    Pages 1-32

About this book

Introduction

This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, the algebras derived from them, and toric varieties. The book discusses several properties and invariants of these objects, such as efficient generation, unimodular triangulations and covers, basic theory of monoid rings, isomorphism problems and automorphism groups, homological properties and enumerative combinatorics. The last part is an extensive treatment of the K-theory of monoid rings, with extensions to toric varieties and their intersection theory.

 

This monograph has been written with a view towards graduate students and researchers who want to study the cross-connections of algebra and discrete convex geometry. While the text has been written from an algebraist's view point, also specialists in lattice polytopes and related objects will find an up-to-date discussion of affine monoids and their combinatorial structure. Though the authors do not explicitly formulate algorithms, the book takes a constructive approach wherever possible.

Winfried Bruns is Professor of Mathematics at Universität Osnabrück.

Joseph Gubeladze is Professor of Mathematics at San Francisco State University.

Keywords

Grad K-theory Lattice algebra commutative algebra discrete geometry

Bibliographic information

  • DOI https://doi.org/10.1007/b105283
  • Copyright Information Springer-Verlag New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-76355-2
  • Online ISBN 978-0-387-76356-9
  • Series Print ISSN 1439-7382
  • About this book
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