The 2-divisibility of divisors on K3 surfaces in characteristic 2
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912076092407808 |
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| author | Katsura, Toshiyuki Kondō, Shigeyuki Schütt, Matthias |
| author_facet | Katsura, Toshiyuki Kondō, Shigeyuki Schütt, Matthias |
| contents | We show that K3 surfaces in characteristic 2 can admit sets of $n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each $n=8,12,16,20$. More precisely, all values occur on supersingular K3 surfaces, with exceptions only at Artin invariants 1 and 10, while on K3 surfaces of finite height, only $n=8$ is possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The 2-divisibility of divisors on K3 surfaces in characteristic 2 Katsura, Toshiyuki Kondō, Shigeyuki Schütt, Matthias Algebraic Geometry Cryptography and Security 14J28 (Primary), 14C20, 14J27 (Secondary) We show that K3 surfaces in characteristic 2 can admit sets of $n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each $n=8,12,16,20$. More precisely, all values occur on supersingular K3 surfaces, with exceptions only at Artin invariants 1 and 10, while on K3 surfaces of finite height, only $n=8$ is possible. |
| title | The 2-divisibility of divisors on K3 surfaces in characteristic 2 |
| topic | Algebraic Geometry Cryptography and Security 14J28 (Primary), 14C20, 14J27 (Secondary) |
| url | https://arxiv.org/abs/2410.14085 |