Olof Bergvall: Cohomology of moduli spaces of Del Pezzo surfaces

Abstract:
A geometric marking of a Del Pezzo surface is a special type of basis for its Picard lattice. There is a Weyl group W acting on the moduli space M of geometrically marked Del Pezzo surfaces of degree d (by changing markings) and we would like to understand the cohomology groups of M as representations of W. We shall see how this can be achieved by comparing two fairly different descriptions of M and its relatives - point sets in the projective plane (over finite fields) and subspace arrangements (of hyperplanes and tori). Parts of the talk are joint work with Jonas Bergström and Frank Gounelas.