Polynomial functors, wreath products and pointed admissible G-covers.

Time: 9:00 - 10h30, 12rd June

Venue: Room 507, A6, Institute of Mathematics

Abstract: I will report on a work in progress aimed at determining recursive formulae for the Betti numbers of the moduli space of admissible G-covers of genus zero curves, where G is a finite group. We follow the approach of Getzler-Kapranov and of Manin to compute the Betti numbers of the moduli space of pointed curves of genus zero (which corresponds to the case where G is the trivial group), using the theory of operads.

For a general G, following Macdonald article “Polynomial functors and wreath products”, we define a composition operation on the Grothendieck group of varieties and we show that the Hodge-Grothendieck characteristic can be used to express the Betti numbers of the moduli space in terms of those of the loci corresponding to covering of the projective line.