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Given a subspace arrangement, there are several De Concini-Procesi modelsassociated to it, depending on distinct sets of initial combinatorial data(building sets). The first goal of this paper is to describe, for the rootarrangements of types A_n, B_n (=C_n), D_n, the poset of all the building setswhich are invariant with respect to the Weyl group action, and therefore toclassify all the wonderful models which are obtained by adding to thecomplement of the arrangement an equivariant divisor. Then we point out, forevery fixed n, a family of models which includes the minimal model and themaximal model; we call these models `regular models' and we compute, in thecomplex case, their Poincar\'e polynomials.

Families of building sets and regular wonderful models