Maximal-unipotent-monodromy fibration conjecture for Calabi–Yau mirrors

Let $X$ be a Calabi–Yau variety, or let $X\setminus D$ be a log Calabi–Yau variety. Suppose that $X$ (or $X\setminus D$) admits a semi-stable degeneration connected to a point of maximal unipotent monodromy, and that the cone over the dual intersection complex of the central fibre has dimension $k$. Maximal-unipotent-monodromy fibration conjecture. The mirror of $X$ (or $X\setminus D$) admits a Calabi–Yau fibration structure with a $k$-dimensional base. This predicts that the combinatorial dimension of a suitable degeneration is reflected by the dimension of the base of a fibration on the mirror; the paper gives examples but does not establish the general claim.