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.