Canonical Artin stacks over log smooth schemes

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...

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Bibliographic Details
Published inMathematische Zeitschrift Vol. 274; no. 3-4; pp. 779 - 804
Main Author Satriano, Matthew
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2013
Subjects
Mathematics
Mathematics and Statistics
Stacky fan
14D23
Log structure
14M25
Chevalley–Shephard–Todd
Toric stack
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ISSN0025-5874
1432-1823
DOI10.1007/s00209-012-1096-7

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Summary: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 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 .
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-012-1096-7