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2016 Inertia groups of a toric Deligne-Mumford stack, fake weighted projective stacks, and labeled sheared simplices
Rebecca Goldin, Megumi Harada, David Johannsen, Derek Krepski
Rocky Mountain J. Math. 46(2): 481-517 (2016). DOI: 10.1216/RMJ-2016-46-2-481

Abstract

This paper determines the inertia groups (isotropy groups) of the points of a toric Deligne-Mumford stack $[Z/G]$ (considered over the category of smooth manifolds) that is realized from a quotient construction using a stacky fan or stacky polytope. The computation provides an explicit correspondence between certain geometric and combinatorial data. In particular, we obtain a computation of the connected component of the identity element $G_0 \subset G$ and the component group $G/G_0$ in terms of the underlying stacky fan, enabling us to characterize the toric DM stacks which are global quotients. As another application, we obtain a characterization of those stacky polytopes that yield stacks equivalent to weighted projective stacks and, more generally, to \textit {`fake' weighted projective stacks}. Finally, we illustrate our results in detail in the special case of \textit {labeled sheared simplices}, where explicit computations can be made in terms of the facet labels.

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Rebecca Goldin. Megumi Harada. David Johannsen. Derek Krepski. "Inertia groups of a toric Deligne-Mumford stack, fake weighted projective stacks, and labeled sheared simplices." Rocky Mountain J. Math. 46 (2) 481 - 517, 2016. https://doi.org/10.1216/RMJ-2016-46-2-481

Information

Published: 2016
First available in Project Euclid: 26 July 2016

zbMATH: 1362.14053
MathSciNet: MR3529080
Digital Object Identifier: 10.1216/RMJ-2016-46-2-481

Subjects:
Primary: 14M25, 57R18
Secondary: 14L24

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

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Vol.46 • No. 2 • 2016
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