The lecture discusses results on how DeConcini-Procesi resolutions
help simplify finite group actions on ${\mathbb R}^n$. The isomorphism
types of the stabilizers of points are chosen as the benchmark for
measuring the degree of simplification. It is shown how, in the case of
the permutation action of the symmetric group, set diagrams on cubes help
explicitely compute the stabilizers of the points in the resolution. In
general, it is proved that, in a suitable resolution, all stabilizers are
isomorphic to a product of the finite groups of size two.

Keywords:

Hyperplane arrangements; group actions; cubic diagrams; stabilizers.

Lecture #10715

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