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arXiv · 2506.15491

On Gorenstein $\mathbb{Q}_p$-rational threefold and fourfold singularities

Jefferson Baudin·Zsolt Patakfalvi·Linus Rösler·Maciej Zdanowicz
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Abstract

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.

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Jefferson Baudin, Zsolt Patakfalvi, Linus Rösler, Maciej Zdanowicz. 2025-06-18. On Gorenstein $\mathbb{Q}_p$-rational threefold and fourfold singularities. https://arxiv.org/abs/2506.15491

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