On deformation method in invariant theory

Dmitri Panyushev

Displaying similar documents to “On deformation method in invariant theory”

Reductive group actions on affine varieties and their doubling

Dmitri I. Panyushev (1995)

Annales de l'institut Fourier

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We study $G$ -actions of the form $(G : X \times X^{*})$ , where $X^{*}$ is the dual (to $X$ ) $G$ -variety. These actions are called the doubled ones. A geometric interpretation of the complexity of the action $(G : X)$ is given. It is shown that the doubled actions have a number of nice properties, if $X$ is spherical or of complexity one.

On classical invariant theory and binary cubics

Gerald W. Schwarz (1987)

Annales de l'institut Fourier

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Let $G$ be a reductive complex algebraic group, and let $C [m V]^{G}$ denote the algebra of invariant polynomial functions on the direct sum of $m$ copies of the representations space $V$ of $G$ . There is a smallest integer $n = n (V)$ such that generators and relations of $C [m V]^{G}$ can be obtained from those of $C [n V]^{G}$ by polarization and restitution for all $m > n$ . We bound and the degrees of generators and relations of $C [n V]^{G}$ , extending results of Vust. We apply our techniques to compute the invariant theory of binary cubics. ...

A generalization of Mumford's geometric invariant theory.

Hausen, Jürgen (2001)

Documenta Mathematica

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Introduction to actions of algebraic groups

Michel Brion (2010)

Les cours du CIRM

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These notes present some fundamental results and examples in the theory of algebraic group actions, with special attention to the topics of geometric invariant theory and of spherical varieties. Their goal is to provide a self-contained introduction to more advanced lectures.

A general Hilbert-Mumford criterion

Jürgen Hausen (2003)

Annales de l’institut Fourier

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Let a reductive group $G$ act on an algebraic variety $X$ . We give a Hilbert-Mumford type criterion for the construction of open $G$ -invariant subsets $V \subset X$ admitting a good quotient by $G$ .

Equidimensional actions of algebraic tori

Haruhisa Nakajima (1995)

Annales de l'institut Fourier

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Let $X$ be an affine conical factorial variety over an algebraically closed field of characteristic zero. We consider equidimensional and stable algebraic actions of an algebraic torus on $X$ compatible with the conical structure. We show that such actions are cofree and the nullcones of $X$ associated with them are complete intersections.