Effective cone conjecture for klt Calabi–Yau pairs

Let $(X,\Delta)$ be a klt Calabi–Yau pair. Let $\mathcal{B}^e(X)$ denote the effective cone appearing in the source, and let $PsAut(X,\Delta)$ act on it by pullback. Effective cone conjecture. There is a rational polyhedral cone $\Pi\subset\mathcal{B}^e(X)$ such that

$$PsAut(X,\Delta)\Pi=\mathcal{B}^e(X),$$

and, for every $g\in PsAut(X,\Delta)$,

$$g^*\Pi^\circ\cap\Pi^\circ\neq\emptyset$$

if and only if $g^*=id$. This conjecture is used to relate the effective cone conjecture to movable-cone questions for product varieties; its resolution status is not specified in the supplied text.