Serrano's strict nefness conjecture for projective manifolds

Let $X$ be a projective manifold of dimension $n$, and let $L$ be a strictly nef line bundle, meaning that $L\cdot C>0$ for every irreducible curve $C\subset X$. Serrano's conjecture. The divisor $K_X+tL$ is ample for every real number $t>n+1$. This conjecture generalizes known results in dimensions two and three; the paper proves it in several higher-dimensional cases, while the remaining cases are open.