Lectures on Invariant Theory (London Mathematical Society Lecture Note Series, Series Number 296)

The 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. The Symbolic Method -- The First Fundamental Theorem -- Reductive Algebraic Groups -- Hilbert's Fourteenth Problem -- Algebra Of Covariants -- Quotients -- Linearization Of Actions -- Stability -- Numerical Criterion Of Stability -- Projective Hypersurfaces -- Configurations Of Linear Subspaces -- Toric Varieties. Igor Dolgachev. Includes Bibliographical References (p. 205-213) And Indexes. 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. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the primary goal of this book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. The style is accessible and there are numerous examples and exercises to aid the reader 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 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises