De Concini-Procesi models of arrangements and symmetric group actions (Publications of the Scuola Normale Superiore)

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.