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 $X_\sg$ is ordinary if and only if $(X,\sg)$ is an ordinary building set. This implies the ordinarity of many other well-known configuration spaces (under suitable assumptions).

2010 Mathematics Subject Classification: 14G17, 14J99

Keywords and Phrases: Ordinary varieties, ordinarity, configuration spaces, wonderful compactification, moduli of n-pointed, stable curves of genus zero.

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