Hybrid toric varieties and the non-archimedean SYZ fibration on Calabi–Yau hypersurfaces

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.