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Beschreibung
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.
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.
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.
Details
Erscheinungsjahr: 2012
Fachbereich: Arithmetik & Algebra
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9780521525480
ISBN-10: 0521525489
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Dolgachev, Igor
Hersteller: Cambridge University Press
Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße: 229 x 152 x 14 mm
Von/Mit: Igor Dolgachev
Erscheinungsdatum: 17.08.2012
Gewicht: 0,393 kg
Artikel-ID: 102517531

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