The F-conjecture for nef divisors on the moduli space of pointed rational curves

Let $\overline{M}_{0,n}$ be the Deligne–Mumford moduli space of stable $n$-pointed rational curves. A line bundle on $\overline{M}_{0,n}$ is F-nef if it has nonnegative intersection with every F-curve, where F-curves are the one-dimensional boundary strata of $\overline{M}_{0,n}$. F-conjecture. A line bundle on $\overline{M}_{0,n}$ is nef if and only if it is F-nef. Equivalently, the nef cone $\operatorname{Nef}(\overline{M}_{0,n})$ is the finite polyhedral cone of F-nef divisor classes. The conjecture gives a combinatorial description of the nef cone and is known for $n\leq 7$, but remains open in general.