The complex and Ricci-flat structure conjecture for the dual torus family

Let $Y$ be a Calabi--Yau manifold with a special Lagrangian $T^n$-fibration, and let ${\cal M}_D(T^n,Y)$ be the family of dual tori over ${\cal M}_{sL}(T^n,Y)$. The dual torus family conjecture. The family ${\cal M}_D(T^n,Y)$ admits complex structures and Ricci-flat Kähler metrics. In particular, it has a nowhere vanishing holomorphic $n$-form. This is presented as the most accessible part of the preceding SYZ compactification conjectures, while the source does not establish it.