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

Abstract

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.