On Serrano’s conjecture on projective bundles

Serrano’s conjecture asserts that if D is a strictly nef divisor on a projective variety X of dimension n, then \(K_X + tD\) $K_X+tD$ is ample for \(t > n + 1\) $t>n+1$ . In this article, we investigate this conjecture for strictly nef divisors on projective bundles over higher dimensional smooth projective varieties.