Special Lagrangian Fibrations, Berkovich Retraction, and Crystallographic Groups

Abstract

Abstract We explicitly construct special Lagrangian fibrations on finite quotients of maximally degenerating abelian varieties and glue these to the Berkovich retraction to form a “hybrid” fibration. We also study their symmetries explicitly that can be regarded as crystallographic groups. In particular, a conjecture of Kontsevich–Soibelman [ 24, Conjecture 3] is solved at an enhanced level for finite quotients of abelian varieties in any dimension.