ScalingStacks

Theorem 1.1. (cf. section 5.4) For the Fermat family, consider the Calabi-Yau metrics on $X_{s}$ in the polarisation class $s^{-1}[\Delta]$ where $[\Delta]$ is a fixed Kähler class on $\mathbb{CP}^{n+1}$ restricted to $X_{s}$. Then for a subsequence of $X_{s}$ as $s\to+\infty$, there exists a special Lagrangian $T^{n}$-fibration on the generic region $U_{s}\subset X_{s}$, such that $\frac{\text{Vol}(U_{s})}{\text{Vol}(X_{s})}\to 1$ as $s\to+\infty$.