Description |
1 online resource (236 pages) |
Series |
London Mathematical Society Lecture Note Series ; no. 296 |
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London Mathematical Society lecture note series ; no. 296.
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Contents |
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 |
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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 |
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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 |
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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 |
Summary |
This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises |
Notes |
Title from publishers bibliographic system (viewed 22 Dec 2011) |
Bibliography |
Includes bibliographical references and index |
Subject |
Invariants.
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Linear algebraic groups.
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Geometry, Differential.
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Geometry, Algebraic.
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MATHEMATICS -- Algebra -- Linear.
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Geometry, Algebraic
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Geometry, Differential
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Invariants
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Linear algebraic groups
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Form |
Electronic book
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ISBN |
9780511615436 |
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0511615434 |
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9780521525480 |
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0521525489 |
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9781107367173 |
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1107367174 |
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9781107362260 |
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1107362261 |
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