Lectures on invariant theory
Author(s)
Bibliographic Information
Lectures on invariant theory
(London Mathematical Society lecture note series, 296)
Cambridge University Press, 2003
- : pbk
Available at 66 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
-
Science and Technology Library, Kyushu University
: pbk411.66/D 84031212010000835,
: pbk.023212003003896 -
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: pbk.S||LMS||29603031035
Note
Includes bibliographical references (p. 205-213) and indexes
Description and Table of Contents
Description
The primary goal of this 2003 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.
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.
by "Nielsen BookData"