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December 2011 Moduli spaces of weighted pointed stable rational curves via GIT
Young-Hoon Kiem, Han-Bom Moon
Osaka J. Math. 48(4): 1115-1140 (December 2011).

Abstract

We construct moduli spaces of weighted pointed stable rational curves $\bar{M}_{0,n \cdot \epsilon}$ with symmetric weight data by the GIT quotient of moduli spaces of weighted pointed stable maps $\bar{M}_{0,n \cdot \epsilon}(\mathbb{P}^{1},1)$. As a consequence, we prove that the Knudsen--Mumford space $\bar{M}_{0,n}$ of $n$-pointed stable rational curves is obtained by a sequence of explicit blow-ups from the GIT quotient $(\mathbb{P}^{1})^{n}\qquotient \mathit{SL}(2)$ with respect to the symmetric linearization $\mathcal{O}(1, \ldots, 1)$. The intermediate blown-up spaces turn out to be $\bar{M}_{0,n \cdot \epsilon}$ for suitable ranges of $\epsilon$. As an application, we provide a new unconditional proof of M. Simpson's theorem about the log canonical models of $\bar{M}_{0,n}$.

Citation

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Young-Hoon Kiem. Han-Bom Moon. "Moduli spaces of weighted pointed stable rational curves via GIT." Osaka J. Math. 48 (4) 1115 - 1140, December 2011.

Information

Published: December 2011
First available in Project Euclid: 11 January 2012

zbMATH: 1253.14029
MathSciNet: MR2871297

Subjects:
Primary: 14H10
Secondary: 14L24

Rights: Copyright © 2011 Osaka University and Osaka City University, Departments of Mathematics

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Vol.48 • No. 4 • December 2011
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