Lectures on Invariant Theory / Edition 1

by Igor Dolgachev

Overview

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.

Product Details

ISBN-13:	9780521525480
Publisher:	Cambridge University Press
Publication date:	08/07/2003
Series:	London Mathematical Society Lecture Note Series , #296
Edition description:	New Edition
Pages:	238
Product dimensions:	5.98(w) x 9.02(h) x 0.55(d)

Table of Contents

1. The symbolic method; 2. The first fundamental theorem; 3. Reductive algebraic groups; 4. Hilbert's fourteenth problem; 5. Algebra of covariants; 6. Quotients; 7. Linearization of actions; 8. Stability; 9. Numerical criterion of stability; 10. Projective hypersurfaces; 11. Configurations of linear subspaces; 12. Toric varieties.

Editorial Reviews

'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

From the Publisher