Modern Birkhäuser classics

"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 volume is an attempt to provide an overview of some of the recent advances in representation theory from a geometric standpoint. A geometrically-oriented treatment is very timely and has long been desired, especially since the discovery of D-modules in the early '80s and the quiver approach to quantum groups in the early '90s.