| Résume | In the SYZ mirror symmetry context, SYZ fibrations are often studied. In particular, it is well known thatthey induce affine structures on their base spaces. On the other hand, Kontsevich and Soibelman introduce a non-Archimedean analog of SYZ fibrations, which is called non-Archimedean SYZ fibrations later. Non-Archimedean SYZ fibrations induce affine structures as well as SYZ fibrations. Moreover, they predict a certain equivalence between SYZ fibrations and non-Archimedean SYZ fibrations for maximally degenerating family of polarized Calabi-Yau varieties. In particular, two affine structures coming from these different origins are expected to coincide. We proved the equivalence for K-trivial finite quotients of polarized abelian varieties by introducing what we call hybrid SYZ fibrations. In this talk, we introduce the above theorem. This talk is based on a joint work (https://arxiv.org/abs/2206.14474) with Yuji Odak. |
