Lectures on Invariant Theory / Igor Dolgachev.
This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises.
Saved in:
| Online Access: |
Full Text (via Cambridge) |
|---|---|
| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2003.
|
| Series: | London Mathematical Society lecture note series ;
no. 296. |
| Subjects: |
MARC
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| 100 | 1 | |a Dolgachev, I. |q (Igor V.) |1 https://id.oclc.org/worldcat/entity/E39PBJyh68B9kPWfFMmXjx3qQq | |
| 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) | ||
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| 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. | |
| 650 | 0 | |a Invariants. | |
| 650 | 0 | |a Linear algebraic groups. | |
| 650 | 0 | |a Geometry, Differential. | |
| 650 | 0 | |a Geometry, Algebraic. | |
| 650 | 7 | |a Geometry, Algebraic |2 fast | |
| 650 | 7 | |a Geometry, Differential |2 fast | |
| 650 | 7 | |a Invariants |2 fast | |
| 650 | 7 | |a Linear algebraic groups |2 fast | |
| 758 | |i has work: |a Lectures on invariant theory (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFxwVmxcwg9JHb3XrXqwyd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |z 9780521525480 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v no. 296. | |
| 856 | 4 | 0 | |u https://colorado.idm.oclc.org/login?url=https://doi.org/10.1017/CBO9780511615436 |z Full Text (via Cambridge) |
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