2 problems

Weak Campana–Peternell conjecture. If the tangent bundle of a Fano manifold is nef, then it is also big.

Greb–Wong–Höring–Peternell conjecture. The tangent bundle $d4af_X$ is nef, respectively big and nef, if and only if some canonical extension $Z_X$ of $X$ is Stein, respectively aff…