ScalingStacks

Theorem 1.3. Let $X\to S\setminus\{0\}$ be an algebraic maximal degeneration family of Calabi-Yau manifolds, with the polarization ample line bundle $L\to X$. Assume the NA MA-real MA comparison property holds for $X$. Given any $0<\delta\ll 1$, for sufficiently small $t$ depending on $\delta$, there exists a special Lagrangian $T^{n}$-fibration with respect to the Calabi-Yau structure $(\omega_{CY,t},\Omega_{t})$ on an open subset of $X_{t}$ whose normalized Calabi-Yau measure is at least $1-\delta$.