Generalized abundance conjecture for Calabi–Yau varieties

Let $X$ be a Calabi–Yau variety, meaning a normal projective variety with only ${\mathbb Q}$-factorial terminal singularities, $h^1(X,{\mathscr O}_X)=0$, and numerically trivial canonical divisor. A divisor on $X$ is nef if it has nonnegative intersection with every curve, and is semi-ample if some positive multiple is basepoint-free. Generalized abundance conjecture. Every nef divisor on a Calabi–Yau variety is semi-ample. The usual abundance conjecture only predicts this for effective nef divisors; the generalized form remains open in dimension three as well and is part of the expected Mori-dream-space-like structure of Calabi–Yau varieties modulo birational automorphisms.