| Résume | For a finite subgroup G of SL(2,C) and for n \geq 1, the Hilbert
scheme X=Hilb^[n](S) of n points on the minimal resolution S of the Kleinian
singularity C^2/G provides a crepant resolution of the symplectic quotient C^
{2n}/G_n, where G_n is the wreath product of G with S_n. I'll explain why every
projective, crepant resolution of C^{2n}/G_n is a quiver variety, and why the
movable cone of X can be described in terms of an extended Catalan hyperplane
arrangement of the root system associated to G by John McKay. These results
extend the algebro-geometric aspects of Kronheimer's hyperkahler description of
S to higher dimensions. This is recent joint work with Gwyn Bellamy.
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