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arXiv · 1302.0385

Global quotients among toric Deligne-Mumford stacks

Megumi Harada·Derek Krepski
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Abstract

This work characterizes global quotient stacks---smooth stacks associated to a finite group acting 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.

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Megumi Harada, Derek Krepski. 2013-02-02. Global quotients among toric Deligne-Mumford stacks. https://arxiv.org/abs/1302.0385

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