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Oberseminar SoSe 2010 Zusammenfassung des Vortrags von S. M. Gusein-Zade (Moskau)

On generating series of classes of equivariant Hilbert schemes of fat points

In some previous papers, there were given formulae for generating series of classes (in the Grothendieck ring of complex quasi-projective varieties) of Hilbert schemes of zero-dimensional subschemes on smooth varieties and on orbifolds in terms of certain local data and the, so called, power structure over the corresponding ring. We give an analogue of these formulae for equivariant (with respect to an action of a finite group on a smooth variety) Hilbert schemes of zero-dimensional subschemes and compute some local generating series for an action of the cyclic group on a smooth surface.
The talk reflects a joint work with I. Luengo and A. Melle.