Hybrid toric varieties and the non-archimedean SYZ fibration on Calabi–Yau hypersurfaces
Abstract
Using a construction by Yamamoto of contraction maps from tropical Calabi-Yau varieties to their dual intersection complex, we construct a non-archimedean SYZ fibration for a class of maximally degenerate hypersurfaces in projective space.We furthermore prove that under a discrete symmetry assumption, the potential for the nonarchimedean Calabi-Yau metric is constant along the fibers of the retraction.The proof uses the work of Li on the Fermat degeneration of hypersurfaces, and an explicit description of toric plurisubharmonic metrics on the hybrid space associated with a complex toric variety.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Algebraic Geometry and Number Theory
Geometry and complex manifolds
Publication details
- Journal / source
- Algebraic geometry
- Publisher
- Foundation Compositio Mathematica
- Pages
- 538–587
- Publication date
- 12 June 2026
- Language
- EN