Nefness criterion for divisors on the iterated blow-up $\mathcal{X}_{n+2,(n-2)}$

Let $S$ be the indexing set used to describe the divisor, and let $D$ be a divisor on $\mathcal{X}_{n+2,(n-2)}$ of the form specified in the source’s general divisor expression. Call $D$ F-nef when all its intersections with the relevant F-curves are nonnegative, equivalently when

$$A_{G,J,L}\geq 0$$

and

$$B_{I,G,J,L}\geq 0$$

for every partition $G\sqcup J\sqcup L=S$ and every partition $I\sqcup G\sqcup J\sqcup L=S$, respectively.

Nefness criterion. The divisor $D$ is nef if and only if these F-nef inequalities hold.

This is presented as a conjectural nef-cone description for the indicated blow-up. The source does not provide a resolution status beyond stating the criterion.