2 problems

Beltrametti–Sommese conjecture. If $D-K_X$ is nef, then $D$ is ample.

Extension conjecture. Then $d\ge b-1$, and $(X,L)\cong (\mathbb{P}(\mathcal{E}),\xi_{\mathbb{P}})$ for an ample vector bundle $\mathcal{E}$ on $Z$, with $p$ equal to the restrictio…