| Document Type
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BL
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| Record Number
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951342
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| Doc. No
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b705712
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| Main Entry
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Dolgachev, I., (Igor V.)
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| Title & Author
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Lectures on Invariant Theory /\ Igor Dolgachev.
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| Publication Statement
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Cambridge :: Cambridge University Press,, 2003.
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| Series Statement
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London Mathematical Society Lecture Note Series ;; no. 296
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| Page. NO
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1 online resource (236 pages)
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| ISBN
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0511615434
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: 0521525489
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: 1107362261
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: 1107367174
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: 9780511615436
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: 9780521525480
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: 9781107362260
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: 9781107367173
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| Notes
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Title from publishers bibliographic system (viewed 22 Dec 2011).
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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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.
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| Abstract
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This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises.
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| Subject
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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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Geometry, Algebraic.
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Geometry, Differential.
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Invariants.
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Linear algebraic groups.
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| Subject
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MATHEMATICS-- Algebra-- Linear.
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| Dewey Classification
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512.5
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| LC Classification
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QA201 .D65 2002
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