Chow Motive of Fulton-MacPherson configuration spaces and wonderful compactifications

Details Chow Motive of Fulton-MacPherson configuration spaces and wonderful compactifications Chow Motive of Fulton-MacPherson configuration spaces and wonderful compactifications

2006-11-15

arxiv.org/abs/math/0611459v2

Mathematics

Algebraic Geometry

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

Scientific paper

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 $X[n]/\frak{S}_n$. A generating function for the Chow groups and for the Chow motive of $X[n]$ is given.

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