Ordinarity of Configuration Spaces and of Wonderful Compactifications

We prove the following: (1) if X is ordinary, the Fulton-MacPherson configuration space X[n] is ordinary for all n; (2) the moduli of stable n-pointed curves of genus zero is ordinary. (3) More generally we show that a wonderful compactification XG is ordinary if and only if (X, G) is an ordinary building set. This implies the ordinarity of many other well-known configuration spaces (under suitable assumptions).