Canonical Artin stacks over log smooth schemes

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 $$X$$ .