Wonderful compactifications of the moduli space of points in affine and projective space
Algebraic Geometry
2017-04-10 v3
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.
Keywords
Cite
@article{arxiv.1604.04194,
title = {Wonderful compactifications of the moduli space of points in affine and projective space},
author = {Patricio Gallardo and Evangelos Routis},
journal= {arXiv preprint arXiv:1604.04194},
year = {2017}
}
Comments
revised version, 39 pages