A note on finite abelian gerbes over toric Deligne-Mumford stacks

TL;DR

This paper investigates conditions under which certain gerbes over toric Deligne-Mumford stacks remain within the class of toric Deligne-Mumford stacks, expanding understanding of their structure and classification.

Contribution

It provides a sufficient condition for gerbes over toric Deligne-Mumford stacks to also be toric Deligne-Mumford stacks, highlighting structural stability.

Findings

Identifies conditions for gerbes to be toric DM stacks

Shows stability of toric structure under certain gerbe constructions

Enhances classification of toric stacks with gerbes

Abstract

Any toric Deligne-Mumford stack is a $\mu$-gerbe over the underlying toric orbifold for a finite abelian group $\mu$. In this paper we give a sufficient condition so that certain kinds of gerbes over a toric Deligne-Mumford stack are again toric Deligne-Mumford stacks.