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Product Identifiers

PublisherCambridge University Press

ISBN-100521525489

ISBN-139780521525480

eBay Product ID (ePID)2341148

Product Key Features

Number of Pages238 Pages

LanguageEnglish

Publication NameLectures on Invariant Theory

Publication Year2003

SubjectAlgebra / Linear, Geometry / Differential, General, Algebra / General, Geometry / Algebraic

TypeTextbook

AuthorIgor Dolgachev

Subject AreaMathematics

SeriesLondon Mathematical Society Lecture Note Ser.

FormatPerfect

Dimensions

Item Height0.6 in

Item Weight12.7 Oz

Item Length9 in

Item Width6 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2002-073456

Reviews'Besides interested graduate students and experts, I recommend the book also to mathematicians and theoretical physicists whose research may require invariant theory, representation theory or algebraic geometry.' Acta Scientiarum Mathematicarum, 'The exposition is very systematic, lucid and sufficiently detailed. it certainly [reflects] the author's passion, versatility, all-round knowledge in mathematics, and mastery as both an active researcher and devoted teacher. It is very gratifying to see this beautiful, modern and still down-to-earth introduction to classical and contemporary invariant theory at the public's disposal ï¿½ ' Zentralblatt fï¿½ athematik, 'The exposition is very systematic, lucid and sufficiently detailed. it certainly [reflects] the author's passion, versatility, all-round knowledge in mathematics, and mastery as both an active researcher and devoted teacher. It is very gratifying to see this beautiful, modern and still down-to-earth introduction to classical and contemporary invariant theory at the public's disposal ...' Zentralblatt für Mathematik, '?The exposition is very systematic, lucid and sufficiently detailed. it certainly [reflects] the author?'s passion, versatility, all-round knowledge in mathematics, and mastery as both an active researcher and devoted teacher. It is very gratifying to see this beautiful, modern and still down-to-earth introduction to classical and contemporary invariant theory at the public?'s disposal ? Zentralblatt f'r Mathematik, ‘The exposition is very systematic, lucid and sufficiently detailed. it certainly [reflects] the author’s passion, versatility, all-round knowledge in mathematics, and mastery as both an active researcher and devoted teacher. It is very gratifying to see this beautiful, modern and still down-to-earth introduction to classical and contemporary invariant theory at the public’s disposal …’Zentralblatt für Mathematik, 'The exposition is very systematic, lucid and sufficiently detailed. it certainly [reflects] the author's passion, versatility, all-round knowledge in mathematics, and mastery as both an active researcher and devoted teacher. It is very gratifying to see this beautiful, modern and still down-to-earth introduction to classical and contemporary invariant theory at the public's disposal â€¦' Zentralblatt fr Mathematik

Dewey Edition21

Series Volume NumberSeries Number 296

IllustratedYes

Dewey Decimal512.5

Table Of Content1. 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.

SynopsisThe primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It 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, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces., Based on lectures given at University of Michigan, Harvard University and Seoul National University, this 2003 book is a brief introduction to the main ideas of algebraic and geometric invariant theory. The emphasis is on concrete examples and there are numerous examples and exercises to aid the reader., 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.

LC Classification NumberQA201 .D65 2002