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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.20010 |
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| _version_ | 1866917511384006656 |
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| author | Baudin, Jefferson Martin, Gebhard |
| author_facet | Baudin, Jefferson Martin, Gebhard |
| contents | Extending Enriques' characterization to algebraically closed fields of characteristic $p \geq 7$, we show that every smooth projective surface $X$ with $h^1(X, \mathcal{O}_X) = 2$ and $p_1(X) = p_2(X) = 1$ is birational to an Abelian surface. This characterization fails if $p \leq 5$, and we give a sharp alternative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20010 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Enriques' characterization of Abelian surfaces in positive characteristic Baudin, Jefferson Martin, Gebhard Algebraic Geometry Extending Enriques' characterization to algebraically closed fields of characteristic $p \geq 7$, we show that every smooth projective surface $X$ with $h^1(X, \mathcal{O}_X) = 2$ and $p_1(X) = p_2(X) = 1$ is birational to an Abelian surface. This characterization fails if $p \leq 5$, and we give a sharp alternative. |
| title | Enriques' characterization of Abelian surfaces in positive characteristic |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2605.20010 |