Moduli spaces of weighted pointed stable rational curves via GIT
Algebraic Geometry
2010-03-29 v2
Abstract
We construct the Mumford-Knudsen space of n pointed stable rational curves by a sequence of explicit blow-ups from the GIT quotient (P^1)^n//SL(2) with respect to the symmetric linearization O(1,...,1). The intermediate blown-up spaces turn out to be the moduli spaces of weighted pointed stable curves for suitable ranges of weights. As an application, we provide a new unconditional proof of M. Simpson's Theorem about the log canonical models of the Mumford-Knudsen space. We also give a basis of the Picard group of the moduli spaces of weighted pointed stable curves.
Keywords
Cite
@article{arxiv.1002.2461,
title = {Moduli spaces of weighted pointed stable rational curves via GIT},
author = {Young-Hoon Kiem and Han-Bom Moon},
journal= {arXiv preprint arXiv:1002.2461},
year = {2010}
}
Comments
An error (Lemma 5.3 in v1) has been corrected.