The SYZ compactification conjecture for dual torus fibrations

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 SYZ compactification conjecture. The family ${\cal M}_D(T^n,Y)$ can be compactified to a manifold $X$ with a proper map

$$\gamma:X\to\overline{{\cal M}}_{sL}(T^n,Y),$$

such that $X$ admits metrics with $\operatorname{SU}(n)$ holonomy for which the fibers over ${\cal M}_{sL}(T^n,Y)$ are special Lagrangian $n$-tori. Moreover, $\gamma$ admits a section

$$\tau:\overline{{\cal M}}_{sL}(T^n,Y)\to X$$

such that its restriction over ${\cal M}_{sL}(T^n,Y)$ is the zero-section of ${\cal M}_D(T^n,Y)$. This is the geometric construction of a mirror Calabi--Yau from the dual special Lagrangian torus fibration; the source leaves the existence and nature of the compactification open.