Osaka Journal of Mathematics

Global quotients among toric Deligne--Mumford stacks

Megumi Harada and Derek Krepski

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Abstract

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

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

Dates
First available in Project Euclid: 24 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1427202880

Mathematical Reviews number (MathSciNet)
MR3326610

Zentralblatt MATH identifier
1321.57037

Subjects
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

Citation

Harada, Megumi; Krepski, Derek. Global quotients among toric Deligne--Mumford stacks. Osaka J. Math. 52 (2015), no. 1, 237--271. https://projecteuclid.org/euclid.ojm/1427202880


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