Conjecture 1.1 . [009B]

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Conjecture 1.1.

Given a 1-parameter maximally degenerate family of polarized $n$ -dimensional Calabi-Yau (CY) manifolds $(X_{t},g_{t},J_{t},\omega_{t},\Omega_{t})$ of holonomy $SU(n)$ over the punctured disc $\mathbb{D}_{t}^{*}$ , then there exist special Lagrangian $T^{n}$ -fibrations on the generic region of $X_{t}$ for $0<|t|\ll 1$ .