The non-big movable divisor conjecture for smooth Calabi–Yau threefolds

Let $X$ be a smooth Calabi–Yau threefold, and let its effective cone be the cone generated by effective divisor classes and its movable cone be the cone generated by divisor classes whose stable base locus has codimension at least two. Non-big movable divisor conjecture. Every divisor class contained in the cone of movable divisors on $X$ is effective. This is a physics-informed conjecture motivated by the behavior of nef and semiample divisors on smooth Calabi–Yau threefolds. It is not resolved by the evidence described here; a counterexample would arise from a smooth fibered Calabi–Yau threefold whose base has an ample, non-effective divisor.