Displaying similar documents to “On the actions of SO(3) on lens space II”

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 .

On quasihomogeneous manifolds – via Brion-Luna-Vust theorem

Marco Andreatta, Jarosław A. Wiśniewski (2003)

Bollettino dell'Unione Matematica Italiana

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We consider a smooth projective variety X on which a simple algebraic group G acts with an open orbit. We discuss a theorem of Brion-Luna-Vust in order to relate the action of G with the induced action of G on the normal bundle of a closed orbit of the action. We get effective results in case G = S ⁢ L ⁢ n and dim ⁡ X ≤ 2 ⁢ n - 2 .