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)
 Publication:

arXiv eprints
 Pub Date:
 December 2008
 arXiv:
 arXiv:0812.0778
 Bibcode:
 2008arXiv0812.0778A
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 20 pages