On a smoothness characterization for good moduli spaces

Let X be a smooth Artin stack with properly stable good moduli space X→πX. The purpose of this paper is to prove that a simple geometric criterion can often characterize when the moduli space X is smooth and the morphism π is flat.

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2024-04, Vol.442, p.109564, Article 109564
Main Authors: Edidin, Dan, Satriano, Matthew, Whitehead, Spencer
Format: Article
Language:English
Subjects:
Chevalley-shephard-Todd theorem
Cofree
Coregular
Geometric invariant theory (GIT)
Good moduli spaces
Purity of the branch locus
Stacks
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Description
Summary:Let X be a smooth Artin stack with properly stable good moduli space X→πX. The purpose of this paper is to prove that a simple geometric criterion can often characterize when the moduli space X is smooth and the morphism π is flat.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2024.109564