Strong abundance for Calabi–Yau manifolds

Let $X$ be a Calabi–Yau manifold and let $L\in H^2(X,\mathbb{Q})$ be a $(1,1)$-class such that

$$(L\cdot C)\geq 0$$

for every algebraic curve $C\subset X$. Strong abundance for Calabi–Yau manifolds. There is a unique morphism with connected fibers $g:X\to B$ onto a normal variety $B$ and an ample class $L_B\in H^2(B,\mathbb{Q})$ such that

$$L=g^*L_B.$$

This strengthens the usual abundance expectation by not assuming that $L$ is effective. The source says that the conjecture becomes harder as the dimension of $B$ decreases, with the elliptic-fibration case corresponding to the preceding numerical questions.