Serrano's conjecture on strictly nef divisors

Let $X$ be a projective variety of dimension $n$, and let $D$ be a strictly nef divisor on $X$, meaning that $D\cdot C>0$ for every irreducible curve $C$ in $X$. Serrano's conjecture. If $D$ is strictly nef, then $K_X+tD$ is ample for every real number $t>n+1$. This is presented as a generalization of the Campana–Peternell conjecture; the paper investigates the assertion for strictly nef divisors on projective bundles over higher-dimensional smooth projective varieties.