Stable affine models for algebraic group actions.

Reichstein, Zinovy; Vonessen, Nikolaus

Displaying similar documents to “Stable affine models for algebraic group actions.”

A generalization of Mumford's geometric invariant theory.

Hausen, Jürgen (2001)

Documenta Mathematica

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On orbits of the automorphism group on an affine toric variety

Ivan Arzhantsev, Ivan Bazhov (2013)

Open Mathematics

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Let X be an affine toric variety. The total coordinates on X provide a canonical presentation $\bar{X} \to X$ of X as a quotient of a vector space $\bar{X}$ by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.

Invariant theory for linear algebraic groups II (char k arbitrary)

A. Fauntleroy (1988)

Compositio Mathematica

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Geometric invariant theory for general algebraic groups

Amassa Fauntleroy (1985)

Compositio 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.

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.

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.