We introduce and study smooth compactifications of the moduli space of nlabeled points with weights in projective space, which have normal crossingsboundary and are defined as GIT quotients of the weighted Fulton-MacPhersoncompactification. We show that the GIT quotient of a wonderful compactificationis also a wonderful compactification under certain hypotheses. We also study aweighted version of the configuration spaces parametrizing n points in affinespace up to translation and homothety. In dimension one, the abovecompactifications are isomorphic to Hassett's moduli space of rational weightedstable curves.
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