Seshadri constants and Gromov widths of toric varieties associated with generalized permutohedra

Abstract

In this paper, we study the Seshadri constants and Gromov widths of polarized toric varieties whose moment polytopes are generalized permutohedra. We show that both invariants coincide with the lattice width of the moment polytope, and provide an explicit formula for them in terms of the defining submodular function.