Moduli spaces of weighted pointed stable rational curves via GIT

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.

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

References in corpus (3)

• On Log Canonical Models of the Moduli Space of Stable Pointed Curves
• Nef divisors on ${\bar{M}}_{0,n}$ from GIT
• Ample divisors on moduli spaces of weighted pointed rational curves, with applications to log MMP for ${\bar{M}}_{0,n}$

Cited by in corpus (6)

• On the biregular geometry of the Fulton-MacPherson compactification
• Conformal blocks divisors on ${\bar{M}}_{0,n}$ from $s{l}_2$
• An outline of the log minimal model program for the moduli space of curves
• Mori's program for the moduli space of pointed stable rational curves
• Revisiting the moduli space of 8 points on ${\mathbb{P}}^1$
• Eigenperiods and the moduli of points in the line