Detecting non-displaceable toric fibers on compact toric manifolds via tropicalizations

Abstract

We provide a combinatorial way to locate non-displaceable Lagrangian toric fibers on any compact toric manifold. By taking the intersection of certain tropicalizations coming from its moment polytope, one can detect all Lagrangian toric fibers having non-vanishing Floer cohomology ([15, 16]). The intersection completely characterizes all non-displaceable toric fibers in some cases including pseudo symmetric smooth Fano varieties ([13])