Nef divisors on ${\bar{M}}_{0,n}$ from GIT

Abstract

We introduce and study the GIT CONE of ${\bar{M}}_{0,n}$, 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 ${\bar{M}}_{0,n}$ 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 arXiv:0709.4037. (Cf. also a different proof by Fedorchuk and Smyth arXiv:0810.1677)

20 pages

References in corpus (2)

• The projective invariants of ordered points on the line
• On Log Canonical Models of the Moduli Space of Stable Pointed Curves

Cited by in corpus (12)

• Moduli spaces of weighted pointed stable rational curves via GIT
• Conformal blocks divisors on ${\bar{M}}_{0,n}$ from $s{l}_2$
• $s{l}_2$ conformal block divisors and the nef cone of ${\bar{M}}_{0,n}$
• Towards Mori's program for the moduli space of stable maps
• GIT and moduli with a twist
• An outline of the log minimal model program for the moduli space of curves
• $s{l}_n$ level 1 conformal blocks divisors on ${\bar{M}}_{0,n}$
• The cone of type A, level one conformal blocks divisors
• Log canonical models for the moduli space of pointed stable rational curves
• Log canonical models for ${\bar{M}}_{g,n}$
• Mori's program for the moduli space of pointed stable rational curves
• Mori's program for ${\bar{M}}_{0,7}$ with symmetric divisors