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  • Book
  • © 1994

Discriminants, Resultants, and Multidimensional Determinants

Birkhäuser
  • The definitive text on eliminator theory

  • Revives the classical theory of resultants and discriminants

  • Presents both old and new results of the theory

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eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-0-8176-4771-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
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  • Tax calculation will be finalised during checkout
Softcover Book USD 149.99
Price excludes VAT (USA)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-x
  2. Introduction

    1. Introduction

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

    1. Front Matter

      Pages 11-11
    2. Projective Dual Varieties and General Discriminants

      • Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 13-47
    3. The Cayley Method for Studying Discriminants

      • Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 48-90
    4. Associated Varieties and General Resultants

      • Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 91-121
    5. Chow Varieties

      • 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. Toric Varieties

      • Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 165-192
    3. Newton Polytopes and Chow Polytopes

      • Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 193-213
    4. Triangulations and Secondary Polytopes

      • Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 214-251
    5. A-Resultants and Chow Polytopes of Toric Varieties

      • Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 252-270
    6. A-Discriminants

      • Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 271-296
    7. Principal A-Determinants

      • Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 297-343
    8. Regular A-Determinants and A-Discriminants

      • Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 344-393
  5. Classical Discriminants and Resultants

    1. Front Matter

      Pages 395-395
    2. Discriminants and Resultants for Polynomials in One Variable

      • Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 397-425
    3. Discriminants and Resultants for Forms in Several Variables

      • Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 426-443
    4. Hyperdeterminants

      • Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky
      Pages 444-479
  6. Back Matter

    Pages 480-523

About this book

"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
  • matrix theory

Reviews

From the reviews:

"The book has developed into an indispensable modern classic, during the past 15 years, and it has initiated a true avalanche of related research activities due to its pioneering and inspiring impact. The steadily large number of quotations, which seems to be ever-flowing, bespeaks the undiminished pacemaking role of this unrivalled source book in various areas of current mathematical research, ranging from algebraic geometry and the general theory of hypergeometric functions up to their recent applications in mathematical physics...

It is and remains the broader, unifying approach combining the classical heritage and the powerful abstract viewpoint of the subject that makes the book under review so timeless, attractive, enlightening, inspiring and virtually invaluable -- a characteristic that will persist for further decades in the future. Besides, the comparatively inexpensive reprint of this classic in paperback form must be seen as another rewarding service to the mathematical community as a whole." –Zentralblatt Math (Review of the Softcover Edition)

"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 (Review of the Hardcover Edition)

"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 (Review of the Hardcover Edition)

"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 (Review of the Hardcover Edition)

"…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 (Review of the Hardcover Edition)

"It is very much representative of the Gelfand school style. … Discriminants, Resultants, and Multidimensional Determinants is currently the most cited on MathSciNet. A perusal of the long list of citations indicates the enormous influence of the book. Many of the citations are clearly in the framework set up by the book." (David P. Roberts, The Mathematical Association of America, October, 2009)

Authors and Affiliations

  • Department of Mathematics, Rutgers University, New Brunswick, USA

    Israel M. Gelfand

  • Department of Mathematics, Northwestern University, Evanston, USA

    Mikhail M. Kapranov

  • Department of Mathematics, Northeastern University, Boston, USA

    Andrei V. Zelevinsky

Bibliographic Information

  • Book Title: Discriminants, Resultants, and Multidimensional Determinants

  • Authors: Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky

  • DOI: https://doi.org/10.1007/978-0-8176-4771-1

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1994

  • Softcover ISBN: 978-0-8176-4770-4

  • eBook ISBN: 978-0-8176-4771-1

  • Edition Number: 1

  • Number of Pages: X, 523

  • Number of Illustrations: 8 b/w illustrations

  • Additional Information: Originally published in the series Mathematics: Theory and Application

  • Topics: Algebra, General Algebraic Systems, Commutative Rings and Algebras, Linear Algebra, Algebraic Geometry

Buying options

eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-0-8176-4771-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 149.99
Price excludes VAT (USA)