Discriminants, Resultants, and Multidimensional Determinants

  • Israel M. Gelfand
  • Mikhail M. Kapranov
  • Andrei V. Zelevinsky

Part of the Mathematics: Theory & Applications book series (MBC)

Table of contents

  1. Front Matter
    Pages i-x
  2. Introduction

    1. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 1-10
  3. General Discriminants and Resultants

    1. Front Matter
      Pages 11-11
    2. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 13-47
    3. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 48-90
    4. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 91-121
    5. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 122-161
  4. A-Discriminants and A-Resultants

    1. Front Matter
      Pages 163-163
    2. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 165-192
    3. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 193-213
    4. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 214-251
    5. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 252-270
    6. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 271-296
    7. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 297-343
    8. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 344-393
  5. Classical Discriminants and Resultants

    1. Front Matter
      Pages 395-395
    2. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 397-425
    3. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 426-443
    4. Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 444-479
  6. Back Matter
    Pages 480-523

About this book

Introduction

"This book revives and vastly expands the classical theory of resultants and discriminants. Most of the main new results of the book have been published earlier in more than a dozen joint papers of the authors. The book nicely complements these original papers with many examples illustrating both old and new results of the theory."—Mathematical Reviews

"Collecting and extending the fundamental and highly original results of the authors, it presents a unique blend of classical mathematics and very recent developments in algebraic geometry, homological algebra, and combinatorial theory." —Zentralblatt Math

"This book is highly recommended if you want to get into the thick of contemporary algebra, or if you wish to find some interesting problem to work on, whose solution will benefit mankind." —Gian-Carlo Rota, Advanced Book Reviews

"…the book is almost perfectly written, and thus I warmly recommend it not only to scholars but especially to students. The latter do need a text with broader views, which shows that mathematics is not just a sequence of apparently unrelated expositions of new theories, … but instead a very huge and intricate building whose edification may sometimes experience difficulties … but eventually progresses steadily." —Bulletin of the American Mathematical Society

Keywords

algebra algebraic geometry elimination theory geometry hyperdeterminants mathematics polytopes resultants variable

Authors and affiliations

  • Israel M. Gelfand
    • 1
  • Mikhail M. Kapranov
    • 2
  • Andrei V. Zelevinsky
    • 3
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA
  2. 2.Department of MathematicsNorthwestern UniversityEvanstonUSA
  3. 3.Department of MathematicsNortheastern UniversityBostonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4771-1
  • Copyright Information Springer Science+Business Media New York 1994
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-8176-4770-4
  • Online ISBN 978-0-8176-4771-1
  • Series Print ISSN 2197-1803
  • Series Online ISSN 2197-1811
  • About this book