The abundance conjecture for canonical sheaves

Let $X$ be a smooth projective variety, and let $\omega_X$ denote its canonical sheaf. A line bundle is semi-ample if some positive tensor power is globally generated; in the formulation here, this means that $\mathcal{L}^{n}$ is globally generated for some $n>0$. Abundance conjecture. The canonical sheaf $\omega_X$ is nef if and only if it is semi-ample. This is a central conjecture in the birational classification of algebraic varieties; the supplied source does not state a resolution, so its status is recorded as open.