Pathological MMP singularities as $α_p$-quotients
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908483102703616 |
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| author | Posva, Quentin |
| author_facet | Posva, Quentin |
| contents | We construct pathological examples of MMP singularities in every positive characteristic using quotients by $α_p$-actions. In particular, we obtain non-$S_3$ terminal singularities, as well as locally stable (respectively stable) families whose general fibers are smooth (respectively klt, Cohen--Macaulay and $F$-injective) and whose special fibers are non-$S_2$. The dimensions of these examples are bounded below by a linear function of the characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pathological MMP singularities as $α_p$-quotients Posva, Quentin Algebraic Geometry We construct pathological examples of MMP singularities in every positive characteristic using quotients by $α_p$-actions. In particular, we obtain non-$S_3$ terminal singularities, as well as locally stable (respectively stable) families whose general fibers are smooth (respectively klt, Cohen--Macaulay and $F$-injective) and whose special fibers are non-$S_2$. The dimensions of these examples are bounded below by a linear function of the characteristic. |
| title | Pathological MMP singularities as $α_p$-quotients |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2501.01179 |