On the properness of the moduli space of stable surfaces over ℤ[1/30]

2023/02/11 by Emelie Arvidsson, Arvidsson, Emelie, Fabio Bernasconi +3
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2302.05651

openalex publication_date 2023/02/11 · openalex created_date 2023/02/15 · openalex updated_date 2026/07/28

Abstract

We show the properness of the moduli stack of stable surfaces over 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 ≠ 2, 3 and 5 which are not log canonical centres.

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