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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 .

Galois covers between K 3 surfaces

Gang Xiao (1996)

Annales de l'institut Fourier

We give a classification of finite group actions on a K 3 surface giving rise to K 3 quotients, from the point of view of their fixed points. It is shown that except two cases, each such group gives rise to a unique type of fixed point set.

Good moduli spaces for Artin stacks

Jarod Alper (2013)

Annales de l’institut Fourier

We develop the theory of associating moduli spaces with nice geometric properties to arbitrary Artin stacks generalizing Mumford’s geometric invariant theory and tame stacks.

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