Kawamata–Morrison Cone Conjecture for Calabi–Yau threefolds

Let $X$ be a Calabi–Yau threefold and let $\operatorname{Aut}(X)$ be the group of automorphisms of $X$. Define

$$\operatorname{Nef}^{e}(X):=\operatorname{Nef}(X)\cap\operatorname{Eff}(X).$$

A rational polyhedral cone is a cone generated by finitely many rational classes, and a fundamental domain for a group action is a region whose translates cover the space up to the usual boundary identifications.

Kawamata–Morrison Cone Conjecture. There exists a rational polyhedral cone $\Pi$ contained in the cone spanned by Chern classes of nef effective Cartier divisors, $\operatorname{Nef}^{e}(X)$, which is a fundamental domain for the action of $\operatorname{Aut}(X)$ on $\operatorname{Nef}^{e}(X)$.

The conjecture is related to the birational geometry of Calabi–Yau threefolds and, in particular, predicts that when $\operatorname{Aut}(X)$ is finite, the cone on which it acts should be rational polyhedral. The source gives no resolution status.