Geometry and Arithmetic

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pp: 1–21

DOI: 10.4171/119-1/1

Nef divisors on $\M_{0,n}$ from GIT

Valery Alexeev[1] and David Swinarski[2]

(1) University of Georgia, Athens, United States
(2) Fordham University, Bronx, USA

We introduce and study the GIT cone of $\overline{M}_{0,n}$, which is generated by the pullbacks of the natural ample line bundles on the GIT quotients $(\mathbb P^1)^n/\!/SL(2)$. We give an explicit formula for these line bundles and prove a number of basic results about the GIT cone. As one application, we prove unconditionally that the log canonical models of $\overline{M}_{0,n}$ with a symmetric boundary divisor coincide with the moduli spaces of weighted curves or with the symmetric GIT quotient, extending the result of Matt Simpson.

Keywords: Moduli spaces of curves, Geometric Invariant Theory, GIT