Proper splittings and projectivity for good moduli spaces

Dori Bejleri; Elden Elmanto; Matthew Satriano

Proper splittings and projectivity for good moduli spaces

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arxiv 2408.11057 v1 pith:KOJGR3SP submitted 2024-08-20 math.AG

Dori Bejleri , Elden Elmanto , Matthew Satriano This is my paper · ORCID

classification math.AG

keywords goodmoduliprojectivityproperspaceamplenessapplicationcovering

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abstract

We show that any good moduli space $\pi : \mathcal{X} \to Y$ has a splitting after a proper, generically finite covering of $Y$. As an application we generalize Koll\'ar's ampleness lemma to give a criterion for projectivity of a good moduli space.

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Root stack valuative criterion for good moduli spaces
math.AG 2025-07 accept novelty 7.0 of 10

The authors prove a root stack valuative criterion for good moduli spaces and reductive gerbes, enabling root-extension of generic points and several arithmetic and moduli applications.

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