Lectures on Invariant Theory (London Mathematical Society Lecture Note Series, Series Number 296) - Softcover

Dolgachev, Igor

Softcover

ISBN 10: 0521525489 ISBN 13: 9780521525480

Publisher: Cambridge University Press, 2003

Synopsis

This introduction to the main ideas of algebraic and geometric invariant theory assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, and the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples that originate in classical algebraic geometry. Written in an accessible style with many examples and exercises, the book offers a novel discussion of possible linearizations of actions and the variation of quotients under the change of linearization.

About this title

Book Description

Based on lectures given at University of Michigan, Harvard University and Seoul National University, the primary goal of this book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. The style is accessible and there are numerous examples and exercises to aid the reader.

Review

'The exposition is very systematic, lucid and sufficiently detailed. it certainly [reflects] the author's passion, versatility, all-round knowledge in mathematics, and mastery as both an active researcher and devoted teacher. It is very gratifying to see this beautiful, modern and still down-to-earth introduction to classical and contemporary invariant theory at the public's disposal ...' Zentralblatt für Mathematik

'Besides interested graduate students and experts, I recommend the book also to mathematicians and theoretical physicists whose research may require invariant theory, representation theory or algebraic geometry.' Acta Scientiarum Mathematicarum

Edition details

• Publisher: Cambridge University Press
• Publication date: 2003
• ISBN 10: 0521525489
• ISBN 13: 9780521525480
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 238