Covering Spaces of Symplectic Toric Orbifolds

TL;DR

This paper investigates the structure of covering spaces in symplectic toric orbifolds, providing a classification and describing their polytopal data, with applications to toric structures on product spaces.

Contribution

It characterizes all symplectic toric orbifold coverings as quotients by finite subgroups and describes the polytopes of toric orbifold bundles in terms of fiber and base polytopes.

Findings

All coverings are quotients of a toric orbifold by a finite subgroup.

The labeled polytope of a toric orbifold bundle is described in terms of fiber and base polytopes.

The study includes the number of toric structures on products of labeled projective spaces.

Abstract

In this article we study covering spaces of symplectic toric orbifolds and symplectic toric orbifold bundles. In particular, we show that all symplectic toric orbifold coverings are quotients of some symplectic toric orbifold by a finite subgroup of a torus. We then give a general description of the labeled polytope of a toric orbifold bundle in terms of the polytopes of the fiber and the base. Finally, we apply our findings to study the number of toric structures on products of labeled projective spaces.