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Fixed points for reductive group actions on acyclic varieties

Martin Fankhauser (1995)

Annales de l'institut Fourier

Let X be a smooth, affine complex variety, which, considered as a complex manifold, has the singular -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 .

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