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Displaying similar documents to “Linear models for reductive group actions on affine quadrics”

Fixed points for reductive group actions on acyclic varieties

Martin Fankhauser (1995)

Annales de l'institut Fourier

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Let X be a smooth, affine complex variety, which, considered as a complex manifold, has the singular ℤ -cohomology of a point. Suppose that G is a complex algebraic group acting algebraically on X . Our main results are the following: if G is semi-simple, then the generic fiber of the quotient map π : X → X / / G contains a dense orbit. If G is connected and reductive, then the action has fixed points if dim X / / G ≤ 3 .

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 × 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.