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 $s\to +\infty$.

arXiv comment44 pages

References in corpus (9)

• Adiabatic limits of Ricci-flat Kahler metrics
• Limits of Calabi-Yau metrics when the Kahler class degenerates
• Kahler geometry on toric manifolds, and some other manifolds with large symmetry
• Nilpotent structures and collapsing Ricci-flat metrics on K3 surfaces
• Integral affine structures on spheres and torus fibrations of Calabi-Yau toric hypersurfaces I
• An extension theorem for Kähler currents
• Complex structure degenerations and collapsing of Calabi-Yau metrics
• Solution to a non-Archimedean Monge-Ampère equation
• SYZ geometry for Calabi-Yau 3-folds: Taub-NUT and Ooguri-Vafa type metrics

Cited by in corpus (5)

• Family Floer program and non-archimedean SYZ mirror construction
• Collapsing geometry with Ricci curvature bounded below and Ricci flow smoothing
• The SYZ mirror symmetry conjecture for del Pezzo surfaces and rational elliptic surfaces
• Family Floer mirror space for local SYZ singularities
• Diameter bounds for degenerating Calabi-Yau metrics