Lectures on Invariant Theory

ISBN-13: 9780521525480 / Angielski / Miękka / 2003 / 238 str.

Igor Dolgachev

Opis

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.

Recenzje

'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

Spis treści

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.