In this thesis we deal with the models of subspace arrangements introduced by De Concini and Procesi. In particular we study their integer cohomology rings, which are torsion free Z-modules of which we find Z-bases. When the considered arrangement is the braid hyperplane arrangement, this leads to the study of the integer cohomology rings of the moduli spaces of n-pointed curves of genus 0 and of their Mumford-Deligne compactifications. We deal with the action of the symmetric group on the cohomology rings: we give explicit formulas for the associated generalized Poincaré series, and provide recursive formulas for the characters.