Equidimensional actions of algebraic tori

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.

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

A. Fauntleroy (1988)

Compositio Mathematica

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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 $G$ .

Geometric invariant theory for general algebraic groups

Amassa Fauntleroy (1985)

Compositio Mathematica

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