On Gorenstein $\mathbb{Q}_p$-rational threefolds and fourfolds
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| Format: | Preprint |
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2025
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| _version_ | 1866909652545961984 |
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| 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 |
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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 |