Osaka Journal of Mathematics

Global quotients among toric Deligne--Mumford stacks

Megumi Harada and Derek Krepski

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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.

Article information

Osaka J. Math., Volume 52, Number 1 (2015), 237-271.

First available in Project Euclid: 24 March 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R18: Topology and geometry of orbifolds 53D20: Momentum maps; symplectic reduction
Secondary: 14M25: Toric varieties, Newton polyhedra [See also 52B20] 14D23: Stacks and moduli problems


Harada, Megumi; Krepski, Derek. Global quotients among toric Deligne--Mumford stacks. Osaka J. Math. 52 (2015), no. 1, 237--271.

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