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Groups, Generators, Syzygies, and Orbits in Invariant Theory
V. L. Popov, Moscow Technical University, Russia

Translations of Mathematical Monographs
1992; 245 pp; softcover
Volume: 100
ISBN-10: 0-8218-5335-X
ISBN-13: 978-0-8218-5335-1
List Price: US$90
Member Price: US$72
Order Code: MMONO/100.S
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The history of invariant theory spans nearly a century and a half, with roots in certain problems from number theory, algebra, and geometry appearing in the work of Gauss, Jacobi, Eisenstein, and Hermite. Although the connection between invariants and orbits was essentially discovered in the work of Aronhold and Boole, a clear understanding of this connection had not been achieved until recently, when invariant theory was in fact subsumed by a general theory of algebraic groups.

Written by one of the major leaders in the field, this book provides an excellent, comprehensive exposition of invariant theory. Its point of view is unique in that it combines both modern and classical approaches to the subject. The introductory chapter sets the historical stage for the subject, helping to make the book accessible to nonspecialists.


Graduate students and research mathematicians interested in invariant theory.


"The book is a good reference for specialists in invariant theory and stimulating for non-experts."

-- Zentralblatt MATH

Table of Contents

  • Introduction
  • Notation and terminology
  • The role of reductive groups in invariant theory
  • Constructive invariant theory
  • The degree of the Poincaré series of the algebra of invariants and a finiteness theorem for representations with free algebra of invariants
  • Syzygies in invariant theory
  • Representations with free modules of covariants
  • A classification of normal affine quasihomogeneous varieties of \(SL_2\)
  • Quasihomogeneous curves, surfaces, and solids
  • Appendices
  • Bibliography
  • Subject index
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