A general Hilbert-Mumford criterion

Jürgen Hausen

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Displaying similar documents to “A general Hilbert-Mumford criterion”

A generalization of Mumford's geometric invariant theory.

Hausen, Jürgen (2001)

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A Hilbert-Mumford criterion for SL₂-actions

Jürgen Hausen (2003)

Colloquium Mathematicae

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Let the special linear group G : = SL₂ act regularly on a ℚ-factorial variety X. Consider a maximal torus T ⊂ G and its normalizer N ⊂ G. We prove: If U ⊂ X is a maximal open N-invariant subset admitting a good quotient U → U ⃫N with a divisorial quotient space, then the intersection W(U) of all translates g · U is open in X and admits a good quotient W(U) → W(U) ⃫G with a divisorial quotient space. Conversely, we show that every maximal open G-invariant subset W ⊂ X admitting a good...

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Olga Chuvashova, Nikolay Pechenkin (2013)

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Let X be an affine T-variety. We study two different quotients for the action of T on X: the toric Chow quotient X/C T and the toric Hilbert scheme H. We introduce a notion of the main component H 0 of H, which parameterizes general T-orbit closures in X and their flat limits. The main component U 0 of the universal family U over H is a preimage of H 0. We define an analogue of a universal family WX over the main component of X/C T. We show that the toric Chow morphism restricted on...

Stable affine models for algebraic group actions.

Reichstein, Zinovy, Vonessen, Nikolaus (2004)

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Reductive group actions on affine varieties and their doubling

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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.

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.

Algebras with finitely generated invariant subalgebras

Ivan V. Arzhantsev (2003)

Annales de l’institut Fourier

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We classify all finitely generated integral algebras with a rational action of a reductive group such that any invariant subalgebra is finitely generated. Some results on affine embeddings of homogeneous spaces are also given.

Challenging problems on affine $n$ -space

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