Moduli spaces of weighted pointed stable rational curves via GIT

Details Moduli spaces of weighted pointed stable rational curves via GIT Moduli spaces of weighted pointed stable rational curves via GIT

2010-02-12

arxiv.org/abs/1002.2461v2

Mathematics

Algebraic Geometry

An error (Lemma 5.3 in v1) has been corrected.

Scientific paper

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.

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