Ebook: Discriminants, Resultants, and Multidimensional Determinants
- Tags: Algebra, General Algebraic Systems, Commutative Rings and Algebras, Linear and Multilinear Algebras Matrix Theory, Algebraic Geometry
- Series: Mathematics: Theory & Applications
- Year: 1994
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
"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
"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
"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
Content:
Front Matter....Pages i-x
Introduction....Pages 1-10
Front Matter....Pages 11-11
Projective Dual Varieties and General Discriminants....Pages 13-47
The Cayley Method for Studying Discriminants....Pages 48-90
Associated Varieties and General Resultants....Pages 91-121
Chow Varieties....Pages 122-161
Front Matter....Pages 163-163
Toric Varieties....Pages 165-192
Newton Polytopes and Chow Polytopes....Pages 193-213
Triangulations and Secondary Polytopes....Pages 214-251
A-Resultants and Chow Polytopes of Toric Varieties....Pages 252-270
A-Discriminants....Pages 271-296
Principal A-Determinants....Pages 297-343
Regular A-Determinants and A-Discriminants....Pages 344-393
Front Matter....Pages 395-395
Discriminants and Resultants for Polynomials in One Variable....Pages 397-425
Discriminants and Resultants for Forms in Several Variables....Pages 426-443
Hyperdeterminants....Pages 444-479
Back Matter....Pages 480-523
"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
Content:
Front Matter....Pages i-x
Introduction....Pages 1-10
Front Matter....Pages 11-11
Projective Dual Varieties and General Discriminants....Pages 13-47
The Cayley Method for Studying Discriminants....Pages 48-90
Associated Varieties and General Resultants....Pages 91-121
Chow Varieties....Pages 122-161
Front Matter....Pages 163-163
Toric Varieties....Pages 165-192
Newton Polytopes and Chow Polytopes....Pages 193-213
Triangulations and Secondary Polytopes....Pages 214-251
A-Resultants and Chow Polytopes of Toric Varieties....Pages 252-270
A-Discriminants....Pages 271-296
Principal A-Determinants....Pages 297-343
Regular A-Determinants and A-Discriminants....Pages 344-393
Front Matter....Pages 395-395
Discriminants and Resultants for Polynomials in One Variable....Pages 397-425
Discriminants and Resultants for Forms in Several Variables....Pages 426-443
Hyperdeterminants....Pages 444-479
Back Matter....Pages 480-523
....