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

MARC

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100 1 |a Dolgachev, I.  |q (Igor V.) 
245 1 0 |a Lectures on Invariant Theory /  |c Igor Dolgachev. 
260 |a Cambridge :  |b Cambridge University Press,  |c 2003. 
300 |a 1 online resource (236 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a London Mathematical Society Lecture Note Series ;  |v no. 296 
500 |a Title from publishers bibliographic system (viewed 22 Dec 2011). 
520 |a This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises. 
504 |a Includes bibliographical references and index. 
505 0 |a 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. 
505 8 |a 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. 
505 8 |a 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. 
505 8 |a 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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650 0 |a Invariants. 
650 0 |a Linear algebraic groups. 
650 0 |a Geometry, Differential. 
650 0 |a Geometry, Algebraic. 
650 6 |a Invariants. 
650 6 |a Groupes linéaires algébriques. 
650 6 |a Géométrie différentielle. 
650 6 |a Géométrie algébrique. 
650 7 |a MATHEMATICS  |x Algebra  |x Linear.  |2 bisacsh 
650 7 |a Geometry, Algebraic.  |2 fast  |0 (OCoLC)fst00940902 
650 7 |a Geometry, Differential.  |2 fast  |0 (OCoLC)fst00940919 
650 7 |a Invariants.  |2 fast  |0 (OCoLC)fst00977982 
650 7 |a Linear algebraic groups.  |2 fast  |0 (OCoLC)fst00999060 
776 0 8 |i Print version:  |z 9780521525480 
830 0 |a London Mathematical Society lecture note series ;  |v no. 296. 
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