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Moduli spaces of weighted pointed stable rational curves via GIT

Research paper by Young-Hoon Kiem, Han-Bom Moon

Indexed on: 26 Mar '10Published on: 26 Mar '10Published in: Mathematics - Algebraic Geometry



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.