On Gorenstein $\mathbb{Q}_p$-rational threefolds and fourfolds

Fuente: arXiv
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Main Authors: Baudin, Jefferson, Patakfalvi, Zsolt, Rösler, Linus, Zdanowicz, Maciej
Format: Preprint
Published: 2025
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_version_ 1866909652545961984
author Baudin, Jefferson
Patakfalvi, Zsolt
Rösler, Linus
Zdanowicz, Maciej
author_facet Baudin, Jefferson
Patakfalvi, Zsolt
Rösler, Linus
Zdanowicz, Maciej
contents We prove that for $n \leq 4$ and $p > 5$, quasi--Gorenstein $F$--pure and $\mathbb{Q}_p$--rational $n$--fold singularities are canonical. This is analogous to the usual fact that rational Gorenstein singularities are canonical. The proof is based on a careful analysis of the dual complex of a dlt modification of a log canonical singularity. The result for $n = 4$ is contingent upon the existence of log resolutions.
format Preprint
id arxiv_https___arxiv_org_abs_2506_15491
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On Gorenstein $\mathbb{Q}_p$-rational threefolds and fourfolds
Baudin, Jefferson
Patakfalvi, Zsolt
Rösler, Linus
Zdanowicz, Maciej
Algebraic Geometry
Primary: 14G17, 14B05, 14F30 Secondary: 14J30, 14J35
We prove that for $n \leq 4$ and $p > 5$, quasi--Gorenstein $F$--pure and $\mathbb{Q}_p$--rational $n$--fold singularities are canonical. This is analogous to the usual fact that rational Gorenstein singularities are canonical. The proof is based on a careful analysis of the dual complex of a dlt modification of a log canonical singularity. The result for $n = 4$ is contingent upon the existence of log resolutions.
title On Gorenstein $\mathbb{Q}_p$-rational threefolds and fourfolds
topic Algebraic Geometry
Primary: 14G17, 14B05, 14F30 Secondary: 14J30, 14J35
url https://arxiv.org/abs/2506.15491