"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."โ{128}{148}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." โ{128}{148}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." โ{128}{148}Gian-Carlo Rota, Advanced Book Reviews "โ{128}ฆthe 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, โ{128}ฆ but instead a very huge and intricate building whose edification may sometimes experience difficulties โ{128}ฆ but eventually progresses steadily." โ{128}{148}Bulletin of the American Mathematical Society
CONTENT
General Discriminants and Resultants -- Projective Dual Varieties and General Discriminants -- The Cayley Method for Studying Discriminants -- Associated Varieties and General Resultants -- Chow Varieties -- A-Discriminants and A-Resultants -- Toric Varieties -- Newton Polytopes and Chow Polytopes -- Triangulations and Secondary Polytopes -- A-Resultants and Chow Polytopes of Toric Varieties -- A-Discriminants -- Principal A-Determinants -- 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
