Beltrametti–Sommese–Wisniewski nef-value fibration conjecture

Let $(X,\mathcal L)$ be a nonsingular polarized variety of dimension $n$, with effective log threshold $\mu(\mathcal L)$ and nef value $\tau(\mathcal L)$. Beltrametti–Sommese–Wisniewski conjecture. If

$$\mu(\mathcal L)>\frac{n+1}{2},$$

then

$$\mu(\mathcal L)=\tau(\mathcal L).$$

The equality implies that the nef-value morphism defines a fibration structure. The source presents this as a conjecture of Beltrametti, Sommese, and Wisniewski; no resolution is given in the supplied text.