Symplectic McKay correspondence

Dmitry Kaledin (Moscow)

Let G be a finite subgroup of SL(n), and assume that the quotient
C^n/G admits a smooth crepant resolution Y. In this situation
the McKay correspondence predicts what the cohomology of Y might
be. There is a precise description purely in terms of the group G
and its action on C^n. The McKay correspondence has been proved
recently by V. Batyrev and by J. Denef-F. Loeser, following an
idea of M. Kontsevich. However, their proof is very abstract and
only gives the ranks of the cohomology groups. In the case when
G preserves a symplectic form on $C^n$, there is an alternative,
completely geometric proof which also gives an explicit basis in
the homology. This will be subject of the talk.

I will explain what ``crepant'' means.