Séminaire de Géométrie Tropicale
Mercredi 13 juin 2018 salle 1525-502
The non-archimedean SYZ fibration
Résumé :
We construct non-archimedean SYZ fibrations for maximally degenerate Calabi-Yau varieties, and we show that they are affinoid torus fibrations away from a codimension two subset of the base. This confirms a prediction by Kontsevich and Soibelman. We also give an explicit description of the induced integral affine structure on the base of the SYZ fibration. Our main technical tool is a study of the structure of minimal dlt-models along one-dimensional strata. This is joint work with Nicaise and Xu. Before explaining our results, I will introduce the background on mirror symmetry and the SYZ fibration in symplectic geometry.