SYZ conjecture for Calabi-Yau hypersurfaces in the Fermat family

Abstract

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 $s\to +\infty$.

44 pages

References in corpus (3)

• Kahler geometry on toric manifolds, and some other manifolds with large symmetry
• Integral affine structures on spheres and torus fibrations of Calabi-Yau toric hypersurfaces I
• SYZ geometry for Calabi-Yau 3-folds: Taub-NUT and Ooguri-Vafa type metrics