GIT Compactifications of $M_{0,n}$ from Conics

Abstract

We study GIT quotients parametrizing n-pointed conics that generalize the GIT quotients $({\mathbb{P}}^1{)}^n//SL2$. Our main result is that ${\overline{M}}_{0,n}$ admits a morphism to each such GIT quotient, analogous to the well-known result of Kapranov for the simpler $({\mathbb{P}}^1{)}^n$ quotients. Moreover, these morphisms factor through Hassett's moduli spaces of weighted pointed rational curves, where the weight data comes from the GIT linearization data.

15 pages, 5 figures; corrected inequality in Lemma 5.1, Int. Math. Res. Notices Vol. 2010

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