Strominger–Yau–Zaslow conjecture for Calabi–Yau hypersurfaces in the Fermat family

We produce special Lagrangian $T^n$-fibrations on the generic regions of some Calabi–Yau hypersurfaces in the Fermat family $X_s = \{Z_0\dots Z_{n+1}+ e^{-s} (Z_0^{n+2}+ \dots + Z_{n+1}^{n+2}) = 0\}\subset \mathbb{CP}^{n+1}$ near the large complex structure limit $s\to \infty$.

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Received 15 January 2020

Accepted 23 May 2021

Published 26 July 2022