Discriminants, Resultants, and Multidimensional Determinants / Edition 1

Discriminants, Resultants, and Multidimensional Determinants / Edition 1

by Israel M. Gelfand, Mikhail Kapranov, Andrei Zelevinsky
     
 

ISBN-10: 0817647708

ISBN-13: 9780817647704

Pub. Date: 04/16/2008

Publisher: Birkhauser Verlag

"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

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Overview

"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

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Product Details

ISBN-13:
9780817647704
Publisher:
Birkhauser Verlag
Publication date:
04/16/2008
Series:
Modern Birkhauser Classics Series
Edition description:
Reprint of the 1994 ed. Softcover reprint of the original 1st ed. 1994
Pages:
523
Product dimensions:
6.10(w) x 9.10(h) x 1.10(d)

Table of Contents

Preface.- Introduction.- General Discriminants and Resultants.- Projective Dual Varieties and General Discriminants.- The Cayley Method of Studying Discriminants.- Associated Varieties and General Resultants.- Chow Varieties.- Toric Varieties.- Newton Polytopes and Chow Polytopes.- Triangulations and Secondary Polytopes.- A-Resultants and Chow Polytopes of Toric Varieties.- A-Discriminants.- Principal A-Discriminants.- Regular A-Determinants and A-Discriminants.- Classical Discriminants and Resultants.- Discriminants and Resultants for Polynomials in One Variable.- Discriminants and Resultants for Forms in Several Variables.- Hyperdeterminants.- Appendix A. Determinants.- Appendix B. A. Cayley: On the Theory of Elimination.- Bibliography.- Notes and References.- List of Notation.- Index

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