Arithmetic and geometric deformations of 3-folds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929267391070208 |
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| author | Bernasconi, Fabio Brivio, Iacopo Filipazzi, Stefano |
| author_facet | Bernasconi, Fabio Brivio, Iacopo Filipazzi, Stefano |
| contents | We show that mixed-characteristic and equi-characteristic small deformations of 3-dimensional canonical (resp. terminal) singularities with perfect residue field of characteristic $p>5$ are canonical (resp. terminal). We discuss applications to arithmetic and geometric families of 3-dimensional Fano varieties and minimal models with canonical singularities. Our results are contingent upon the existence of log resolutions of 4-folds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06036 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Arithmetic and geometric deformations of 3-folds Bernasconi, Fabio Brivio, Iacopo Filipazzi, Stefano Algebraic Geometry Primary: 14B07, 14E30, 14G17, Secondary: 14J10 We show that mixed-characteristic and equi-characteristic small deformations of 3-dimensional canonical (resp. terminal) singularities with perfect residue field of characteristic $p>5$ are canonical (resp. terminal). We discuss applications to arithmetic and geometric families of 3-dimensional Fano varieties and minimal models with canonical singularities. Our results are contingent upon the existence of log resolutions of 4-folds. |
| title | Arithmetic and geometric deformations of 3-folds |
| topic | Algebraic Geometry Primary: 14B07, 14E30, 14G17, Secondary: 14J10 |
| url | https://arxiv.org/abs/2303.06036 |