Lectures on Invariant Theory /

This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Dolgachev, I. (Igor V.)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2003.
Colección:London Mathematical Society lecture note series ; no. 296.
Temas:
Invariants.
Linear algebraic groups.
Geometry, Differential.
Geometry, Algebraic.
Groupes linéaires algébriques.
Géométrie différentielle.
Géométrie algébrique.
MATHEMATICS > Algebra > Linear.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title
  • Copyright
  • Dedication
  • Preface
  • Introduction
  • 1 The symbolic method
  • 1.1 First examples
  • 1.2 Polarization and restitution
  • 1.3 Bracket functions
  • Bibliographical notes
  • Exercises
  • 2 The First Fundamental Theorem
  • 2.1 The omega-operator
  • 2.2 The proof
  • 2.3 Grassmann varieties
  • 2.4 The straightening algorithm
  • Bibliographical notes
  • Exercises
  • 3 Reductive algebraic groups
  • 3.1 The Gordan-Hilbert Theorem
  • 3.2 The unitary trick
  • 3.3 Affine algebraic groups
  • 3.4 Nagata's Theorem
  • Bibliographical notes
  • Exercises.
  • 4 Hilbert's Fourteenth Problem
  • 4.1 The problem
  • 4.2 The Weitzenb ock Theorem
  • 4.3 Nagata's counterexample
  • Bibliographical notes
  • Exercises
  • 5 Algebra of covariants
  • 5.1 Examples of covariants
  • 5.2 Covariants of an action
  • 5.3 Linear representations of reductive groups
  • 5.4 Dominant weights
  • 5.5 The Cayley-Sylvester formula
  • 5.6 Standard tableaux again
  • Bibliographical notes
  • Exercises
  • 6 Quotients
  • 6.1 Categorical and geometric quotients
  • 6.2 Examples
  • 6.3 Rational quotients
  • Bibliographical notes
  • Exercises
  • 7 Linearization of actions.
  • 7.1 Linearized line bundles
  • 7.2 The existence of linearization
  • 7.3 Linearization of an action
  • Bibliographical notes
  • Exercises
  • 8 Stability
  • 8.1 Stable points
  • 8.2 The existence of a quotient
  • 8.3 Examples
  • Bibliographical notes
  • Exercises
  • 9 Numerical criterion of stability
  • 9.1 The function æ(x, .)
  • 9.2 The numerical criterion
  • 9.3 The proof
  • 9.4 The weight polytope
  • 9.5 Kempf-stability
  • Bibliographical notes
  • Exercises
  • 10 Projective hypersurfaces
  • 10.1 Nonsingular hypersurfaces
  • 10.2 Binary forms
  • 10.3 Plane cubics
  • 10.4 Cubic surfaces.
  • Bibliographical notes
  • Exercises
  • 11 Configurations of linear subspaces
  • 11.1 Stable configurations
  • 11.2 Points in Pn
  • 11.3 Lines in P3
  • Bibliographical notes
  • Exercises
  • 12 Toric varieties
  • 12.1 Actions of a torus on an affine space
  • 12.2 Fans
  • 12.3 Examples
  • Bibliographical notes
  • Exercises
  • Bibliography
  • Index of Notation
  • Index.

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