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

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.