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arXiv · 1604.04194

Wonderful compactifications of the moduli space of points in affine and projective space

Patricio Gallardo·Evangelos Routis
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Abstract

We introduce and study smooth compactifications of the moduli space of n labeled points with weights in projective space, which have normal crossings boundary and are defined as GIT quotients of the weighted Fulton-MacPherson compactification. We show that the GIT quotient of a wonderful compactification is also a wonderful compactification under certain hypotheses. We also study a weighted version of the configuration spaces parametrizing n points in affine space up to translation and homothety. In dimension one, the above compactifications are isomorphic to Hassett's moduli space of rational weighted stable curves.

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Patricio Gallardo, Evangelos Routis. 2016-04-14. Wonderful compactifications of the moduli space of points in affine and projective space. https://arxiv.org/abs/1604.04194

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