Lectures on Invariant Theory

Lectures on Invariant Theory

Author: Igor Dolgachev

Publisher: Cambridge University Press

ISBN: 0521525489

Category: Mathematics

Page: 244

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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.
Lectures on Invariant Theory
Language: en
Pages: 244
Authors: Igor Dolgachev
Categories: Mathematics
Type: BOOK - Published: 2003-08-07 - Publisher: Cambridge University Press

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
Invariant Theory in All Characteristics
Language: en
Pages: 308
Authors: Harold Edward Alexander Eddy Campbell, David L. Wehlau
Categories: Science
Type: BOOK - Published: - Publisher: American Mathematical Soc.

This volume includes the proceedings of a workshop on Invariant Theory held at Queen's University (Ontario). The workshop was part of the theme year held under the auspices of the Centre de recherches mathematiques (CRM) in Montreal. The gathering brought together two communities of researchers: those working in characteristic 0
Multiplicative Invariant Theory
Language: en
Pages: 200
Authors: Martin Lorenz
Categories: Mathematics
Type: BOOK - Published: 2005-03-10 - Publisher: Springer Science & Business Media

Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage. The present text offers a coherent account of the basic results achieved thus far.. Multiplicative invariant theory is intimately tied to integral representations of finite groups. Therefore,
Geometric Invariant Theory
Language: en
Pages: 314
Authors: David Mumford, John Fogarty, Frances Kirwan
Categories: Mathematics
Type: BOOK - Published: 1994 - Publisher: Springer Science & Business Media

"Geometric Invariant Theory" by Mumford/Fogarty (the firstedition was published in 1965, a second, enlarged editonappeared in 1982) is the standard reference on applicationsof invariant theory to the construction of moduli spaces.This third, revised edition has been long awaited for by themathematical community. It is now appearing in a completelyupdated and
Computational Invariant Theory
Language: en
Pages: 366
Authors: Harm Derksen, Gregor Kemper
Categories: Mathematics
Type: BOOK - Published: 2015-12-23 - Publisher: Springer

This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner