Synopses & Reviews
Brief introduction to algebraic and geometric invariant theory with numerous examples and exercises.
Synopsis
Includes bibliographical references (p. 205-213) and index.
Synopsis
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.
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.