Chow Motive of Fulton-MacPherson configuration spaces and wonderful compactifications

Abstract

We study the Chow groups and the Chow motives of the wonderful compactifications $Y_{\mathcal{G}}$ of arrangements of subvarieties. We prove a natural decomposition of the Chow motive of $Y_{\mathcal{G}}$, in particular of the Fulton-MacPherson configuration space $X[n]$. As a consequence, we prove a decomposition of the Chow motive of $X[n]/{\mathfrak{S}}_n$. A generating function for the Chow groups and for the Chow motive of $X[n]$ is given.

36 pages, presentation is improved, to appear in the Michigan Mathematical Journal