Ample divisors on moduli spaces of weighted pointed rational curves, with applications to log MMP for $\bar{M}_{0,n}$

Abstract

We introduce a new technique for proving positivity of certain divisor classes on $\bar{M}_{0,n}$ and its weighted variants. Our methods give an unconditional description of the spaces of symmetric weighted pointed rational curves as log canonical models of $\bar{M}_{0,n}$.