Koike's infinite-type conjecture for semi-positive hypersurfaces

Let $X$ be a complex manifold and let $Y$ be a non-singular compact Kähler hypersurface of $X$. Assume that the normal bundle $N_{Y/X}$ is topologically trivial and that the line bundle $[Y]$ associated with $Y$ is semi-positive. Koike's infinite-type conjecture. The pair $(Y,X)$ is of infinite type. This predicts infinite Ueda type in the general-dimensional hypersurface setting; the paper motivates it using known results and presents it as a problem for further study, so its general validity remains open.