The nef-cone conjecture for codimension-two classes on the compactification of A_3

Let $\overline{{\mathcal A}_{3}}$ be the toroidal compactification, and let $L$, $M$, and $\beta_2$ be the classes used in the paper. Define

$$F_1=-72L^2+12LM+3M^2+\beta_2,\qquad F_2=72L^2-8LM+M^2-\beta_2.$$

Nef-cone conjecture. The cone of nef codimension-two classes is

$$\operatorname{Nef}^{2}(\overline{{\mathcal A}_{3}})={\mathbb R}_{\ge 0}L^2+{\mathbb R}_{\ge 0}LM+{\mathbb R}_{\ge 0}M^2+{\mathbb R}_{\ge 0}F_1+{\mathbb R}_{\ge 0}F_2.$$

The source states that this is equivalent to the main effective-cone conjecture; it remains unresolved because generation of the pseudoeffective cone by the five surfaces has not been proved.