F-conjecture for $\overline{\mathrm{M}}_{0,n}$

Let $\overline{\mathrm{M}}_{0,n}$ be the moduli space of genus $0$ stable pointed curves. An effective divisor $D=\sum b_I B_I$ on $\overline{\mathrm{M}}_{0,n}$ is F-nef if $D\cdot F\geq 0$ for every F-curve $F$.

F-conjecture. A divisor on $\overline{\mathrm{M}}_{0,n}$ is nef if and only if it is F-nef.

This is the divisor-theoretic form of Fulton’s conjecture that the Mori cone is generated by F-curves. It was shown for $n\leq 7$ by Keel and McKernan in characteristic $0$, but remains open for larger $n$.