Log version of Serrano's conjecture

Let $(X,\Delta)$ be a projective log canonical pair of dimension $n$, and let $L$ be a strictly nef Cartier divisor on $X$. Log version of Serrano's conjecture. The $\mathbb Q$-Cartier divisor

$$K_X+\Delta+tL$$

is ample for every $t>2n$. This is a log generalization of Serrano's conjecture and is presented as a workable version for mild singularities; the paper studies important special cases in dimensions three and four, while the general statement remains open.