2 problems

Let $X$ be a connected compact Kähler manifold, and let $Y$ be a nonsingular hypersurface of $X$ whose normal bundle $N_{Y/X}=[Y]|_Y$ is unitary flat. Here $[Y]$ denotes the holomo…

Semipositivity conjecture. The line bundle $[Y]$ admits a $C^\infty$ Hermitian metric with semi-positive curvature if and only if the pair $(Y,X)$ is of type $(\beta)$.