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

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arxiv 2506.15491 v3 pith:BL3YBOLT submitted 2025-06-18 math.AG

Jefferson Baudin , Zsolt Patakfalvi , Linus Rösler , Maciej Zdanowicz This is my paper · ORCID
classification math.AG
keywords canonicalrationalsingularitiesgorensteinmathbbanalogousanalysiscareful
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension

    math.AG 2025-07 conditional novelty 7.0 of 10

    Smooth proper weakly ordinary varieties of maximal Albanese dimension satisfy chi(X, omega_X) >= 0, with chi = 0 for non-general-type examples and the Albanese image then fibered by ordinary abelian varieties.

  2. Generic vanishing theory in positive characteristic

    math.AG 2025-07 conditional novelty 5.0 of 10

    The paper proves an equivalence between Cartier crystals and V-crystals on dual abelian varieties and derives H^0(X,ω_X)≠0, with S^0(X,ω_X)≠0 in the ordinary case, for normal proper varieties of maximal Albanese dimension.

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