We can also mention two other major open problems :

• The abundance conjecture, stating that if a $K_X+\Delta$ is klt and nef, then it is semi-ample (a multiple has no base-point)

• The Griffith's conjecture : if $E$ is an ample vector bundle over a compact complex manifold, then it is Griffith-positive. (this is known for line bundles of course)