Abstract
We develop a theory of toric Artin stacks extending the theories of toric Deligne–Mumford stacks developed by Borisov–Chen–Smith, Fantechi–Mann–Nironi, and Iwanari. We also generalize the Chevalley–Shephard–Todd theorem to the case of diagonalizable group schemes. These are both applications of our main theorem which shows that a toroidal embedding \(X\) is canonically the good moduli space (in the sense of Alper) of a smooth log smooth Artin stack whose stacky structure is supported on the singular locus of \(X\).
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Acknowledgments
I would like to thank Dan Abramovich, Bhargav Bhatt, Ishai Dan-Cohen, Anton Geraschenko, Arthur Ogus, and Shenghao Sun for many helpful conversations. It is a pleasure to thank my advisor, Martin Olsson, whose guidance and inspiration greatly shaped this paper. Lastly, I thank the anonymous referee for his enthusiastic comments and helpful suggestions.
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Satriano, M. Canonical Artin stacks over log smooth schemes. Math. Z. 274, 779–804 (2013). https://doi.org/10.1007/s00209-012-1096-7
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DOI: https://doi.org/10.1007/s00209-012-1096-7