Giovanni Gaiffi
(SNS Pisa)
Combinatorics of real and complex models of arrangements
Abstract: Given a real subspace arrangement, we will investigate the relations between its DeConcini-Procesi complex models and certain real models which are smooth manifolds with corners. It turns out that there are smooth surjective maps from the real models to the real points of complex models: the combinatorics of the boundary of the models controls the combinatorial properties of these maps.
As an example, we will focus on the braid arrangement of dimension n. In this case, the simplest DeConcini-Procesi model is the moduli space \bar M_{0,n+2} of stable (n+2)-pointed genus 0 curves while the simplest real model is a manifold from which we can recover the geometry of Kapranov's permutoassociahedron.