We show the properness of the moduli stack of stable surfaces over \mathbb{Z}\left[ {1/30} \right], assuming the locally-stable reduction conjecture for stable surfaces. This relies on a local Kawamata–Viehweg vanishing theorem for 3-dimensional log canonical singularities at closed point of characteristic p \ne 2,3 and 5, which are not log canonical centres.
On the properness of the moduli space of stable surfaces over $\mathbb{Z}$ [1/30] / Arvidsson, Emelie; Bernasconi, Fabio; Patakfalvi, Zsolt. - In: MODULI. - ISSN 2949-7647. - (2024). [10.1112/mod.2024.1]
On the properness of the moduli space of stable surfaces over $\mathbb{Z}$ [1/30]
Fabio Bernasconi
;Zsolt Patakfalvi
2024
Abstract
We show the properness of the moduli stack of stable surfaces over \mathbb{Z}\left[ {1/30} \right], assuming the locally-stable reduction conjecture for stable surfaces. This relies on a local Kawamata–Viehweg vanishing theorem for 3-dimensional log canonical singularities at closed point of characteristic p \ne 2,3 and 5, which are not log canonical centres.File allegati a questo prodotto
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