Seminari del Dipartimento di Matematica

Seminario del 2016

Giovanni Gaiffi

Models of reflection arrangements and related combinatorial structures

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

analisi matematica

Let us consider, in a real or complex vector space V, an hyperplane arrangement A whose hyperplanes generate a (real or complex) finite reflection group W. We will focus on the combinatorial properties of the De Concini-Procesi models associated with A (for instance, if A is the braid arrangement, and therefore W = Sn, the minimal complex De Concini-Procesi model associated to it is the moduli space of stable genus 0 curves with n + 1 points). We will point out a combinatorial action of a "big" symmetric group on the boundary strata of these models and we will show how this action leads to find non recursive formulas for the computation of Betti numbers of the models and of the faces of some polytopes (nestohedra) associated to this construction.