The log Campana–Peternell conjecture

Let $(X,\Delta)$ be a klt pair, where $X$ is a normal projective variety and $\Delta$ is an effective $\mathbb{Q}$-divisor such that $K_X+\Delta$ is $\mathbb{Q}$-Cartier. A divisor is strictly nef if it has positive intersection with every curve. The log Campana–Peternell conjecture. If $-(K_X+\Delta)$ is strictly nef, then $-(K_X+\Delta)$ is ample. This is the logarithmic analogue of the Campana–Peternell conjecture. The statement is known in several low-dimensional and special cases, including dimension two, but remains open in general.