Semiampleness criteria for divisors on $\overline M_{0,n}$
  We develop new characteristic-independent combinatorial criteria for semiampleness of divisors on $\overline{M}_{0,n}$. As an application, we associate to a cyclic rational quadratic form satisfying a certain balancedness condition an infinite sequence of semiample line bundles. We also give several sufficient and effective conditions for a symmetric divisor on $\overline{M}_{0,n}$ to be semiample or nef. 
Maksym Fedorchuk
math.AG math.CO math.OC