On the properness of the moduli space of stable surfaces over $\mathbb{Z}[1/30]$

Emelie Arvidsson; Fabio Bernasconi; Zsolt Patakfalvi

On the properness of the moduli space of stable surfaces over $\mathbb{Z}[1/30]$

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arxiv 2302.05651 v2 pith:WMFJX565 submitted 2023-02-11 math.AG

Emelie Arvidsson , Fabio Bernasconi , Zsolt Patakfalvi This is my paper · ORCID

classification math.AG

keywords stablesurfacescanonicalmathbbmodulipropernessassumingcentres

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abstract

We show the properness of the moduli stack of stable surfaces over $\mathbb{Z}[1/30]$, assuming the locally-stable reduction conjecture for stable surfaces. This relies on a local Kawamata--Viehweg vanishing theorem for for 3-dimensional log canonical singularities at closed point of characteristic $p \neq 2, 3$ and $5$ which are not log canonical centres.

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Pathological MMP singularities as $\alpha_p$-quotients
math.AG 2025-01 conditional novelty 8.0 of 10

For every positive characteristic, the author constructs non-S3 terminal singularities of dimension p+1 and stable families with klt, Cohen-Macaulay, F-injective general fibers but non-S2 special fibers.

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