Lectures on Invariant Theory

Klappentext 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. Zusammenfassung Based on lectures given at University of Michigan! Harvard University and Seoul National University! this 2003 book is a brief introduction to the main ideas of algebraic and geometric invariant theory. The emphasis is on concrete examples and there are numerous examples and exercises to aid the reader. Inhaltsverzeichnis 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.

Product details

• Authors: Igor Dolgachev, Igor V. Dolgachev
• Publisher: Cambridge University Press Academic
• Languages: English
• Product format: Paperback / Softback
• Released: 07.08.2003
• EAN: 9780521525480
• ISBN: 978-0-521-52548-0
• Dimensions: 154 mm x 231 mm x 15 mm
• Series: Print On Demand; London Mathematical Society Le; Print on Demand
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra