Inseparable Kummer surfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929264760193024 |
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| author | Matsumoto, Yuya |
| author_facet | Matsumoto, Yuya |
| contents | We introduce an inseparable version of Kummer surfaces. It is defined as a supersingular K3 surface in characteristic 2 with 16 smooth rational curves forming a certain configuration and satisfying a suitable divisibility condition. The main result is that such a surface admits an inseparable double covering by a non-normal surface $A$ that is similar to abelian surfaces in two aspects: its numerical invariants are the same as abelian surfaces, and its smooth locus admits an abelian group structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02770 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inseparable Kummer surfaces Matsumoto, Yuya Algebraic Geometry 14J28 (Primary) 14L15, 14J17, 14B15 (Secondary) We introduce an inseparable version of Kummer surfaces. It is defined as a supersingular K3 surface in characteristic 2 with 16 smooth rational curves forming a certain configuration and satisfying a suitable divisibility condition. The main result is that such a surface admits an inseparable double covering by a non-normal surface $A$ that is similar to abelian surfaces in two aspects: its numerical invariants are the same as abelian surfaces, and its smooth locus admits an abelian group structure. |
| title | Inseparable Kummer surfaces |
| topic | Algebraic Geometry 14J28 (Primary) 14L15, 14J17, 14B15 (Secondary) |
| url | https://arxiv.org/abs/2403.02770 |