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

• Valery Alexeev

University of Georgia, Athens, United States
• David Swinarski

Fordham University, Bronx, USA

A subscription is required to access this book chapter.

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.