Families of building sets and regular models

Given a subspace arrangement, there are several De Concini– Procesi models associated to it, depending on distinct sets of initial combinatorial data (building sets). The first goal of this paper is to describe, for the Coxeter arrangements of types An, Bn (= Cn), Dn, the poset of all the building sets which are invariant with respect to the Weyl group action, and therefore to classify all the models which are obtained by adding to the complement of the arrangement an equivariant divisor. Then, for every fixed n, a family of n − 1 regular models emerges from the picture; we compute, in the complex case, their Poincaré polynomials.