Abundance conjecture for rational nef classes on projective Calabi–Yau manifolds

Let $X$ be a projective Calabi–Yau manifold of dimension $n$, and let $[\alpha]\in\overline{\mathcal{C}}$ be a nef class satisfying

$$\int_X\alpha^n=0$$

and $[\alpha]\in H^2(X,\mathbb{Q})$. A nef class is semiample when it arises from a holomorphic fibration in the sense described in the source.

Abundance conjecture. The class $[\alpha]$ is semiample.

This is a well-known conjecture in algebraic geometry. The source states that it remains open starting in dimension $3$.