The minimal fibering degree of a toric variety equals the lattice width of its polytope

TL;DR

This paper establishes that the minimal fibering degree of a projective toric variety is equal to the lattice width of its associated polytope, providing a complete answer to a recent open question and extending gonality results to higher dimensions.

Contribution

It proves the equality between the minimal fibering degree and lattice width for any projective toric variety, generalizing previous curve gonality results to higher dimensions.

Findings

Minimal fibering degree equals lattice width for toric varieties

Provides a higher dimensional analogue of gonality computations

Answers a recent open question in toric geometry

Abstract

The purpose of this paper is to compute the minimal fibering degree of an arbitrary projective toric variety. We prove that it equals the lattice width of the associated polytope. This gives a complete answer to a question asked in a recent paper of Levinson, Ullery and the second author. The minimal fibering degree of a polarized projective variety was introduced in that paper in order to compute the degree of irrationality (a generalization of gonality) of high degree divisors. From this perspective, our paper gives a higher dimensional analogue of results of Kawaguchi and others who computed the gonality of curves in toric surfaces in terms of lattice widths.