Journal Article

A “Bottom Up” Characterization of Smooth Deligne–Mumford Stacks

Anton Geraschenko and Matthew Satriano

in International Mathematics Research Notices

Volume 2017, issue 21, pages 6469-6483
Published in print November 2017 | ISSN: 1073-7928
Published online September 2016 | e-ISSN: 1687-0247 | DOI: http://dx.doi.org/10.1093/imrn/rnw201
A “Bottom Up” Characterization of Smooth Deligne–Mumford Stacks

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Abstract

We prove a structure theorem for relative coarse space morphisms from smooth Deligne–Mumford stacks, showing that each such map can be decomposed in terms of root stack and canonical stack morphisms. We explain how our result can be understood locally in terms of pseudo-reflections. Lastly, we give an application to equivariant [math]-theory, give several examples illustrating our result, and pose some related questions.

Journal Article.  5814 words. 

Subjects: Mathematics ; Pure Mathematics

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