GLOBAL QUOTIENTS AMONG TORIC DELIGNE-MUMFORD STACKS

This work characterizes global quotient stacks-smooth stacks associated to a finite group acting on a manifold-among smooth quotient stacks [M/G], where M is a smooth manifold equipped with a smooth proper action by a Lie group G. The characterization is described in terms of the action of the connected component G(0) on M and is related to (stacky) fundamental group and covering theory. This characterization is then applied to smooth toric Deligne-Mumford stacks, and global quotients among toric DM stacks are then characterized in terms of their associated combinatorial data of stacky fans.