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Hilbert schemes of points and power structure over the Grothendieck ring of varieties

Le : 09/02/2006 11h00
Par : Eugeny Gorsky (IUM, Moscou et ENS)
Lieu :
Lien web :
Résumé : The Hilbert scheme of points X^{[n]} on a complex projective variety X parametrizes zero-dimensional subschemes of length n on X. It can be considered as one of the basic examples of moduli spaces.This talk, based on the paper of S. M. Gusein-Zade, I. Luengo and A. Melle-Hernandez, provides a way to derive some numerical invariants of X^{[n]} (Euler characteristic, Betti numbers, Hodge-Deligne numbers) in terms of invariants of X. It represents the results of L.Gottsche and J.Cheah in somewhat different terms. The main tool is the power structure over the Grothendieck (semi)ring of complex quasi-projective varieties, constructed by the authors