Ordinarity of configuration spaces and of wonderful compactifications

Details Ordinarity of configuration spaces and of wonderful compactifications Ordinarity of configuration spaces and of wonderful compactifications

2010-05-17

arxiv.org/abs/1005.3005v1

Mathematics

Algebraic Geometry

Scientific paper

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).

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