Toroidal boundary singularities conjecture for Calabi–Yau mirror moduli

Let ${\cal M}$ be a moduli space of complex structures on an $n$-dimensional Calabi–Yau variety $W$, and let ${\cal M}'$ be a moduli space for a mirror Calabi–Yau variety $W'$. Let $NS(W)_{\bf C}$ be the complexified Néron–Severi space of $W$, and consider cusp points corresponding to maximal degenerations in a good moduli space. Toroidal boundary singularities conjecture. Singularities at cusp points of maximal degeneration of a good moduli space for the Calabi–Yau mirrors $W'$ should have toroidal structure defined by natural subcones of the cone of effective divisors in $NS(W)_{\bf C}$. This predicts a toroidal, cone-theoretic description of boundary singularities in mirror moduli spaces; the source does not state which moduli spaces are covered or give resolution evidence.