Lectures on Invariant Theory

Erscheinungsjahr 2012
ISBN: 978-0-521-52548-0
Verlag: Cambridge University Press

Buch, Englisch, Band 296, 236 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 393 g

Reihe: London Mathematical Society Lecture Note Series

The primary goal of this book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It 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, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.

Autoren/Hrsg.

Dolgachev, Igor

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Algebra Elementare Algebra

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.