Unirational quasi-hyperelliptic surfaces in characteristic five
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915461459869696 |
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| author | Ito, Hiroyuki Takayashiki, Shota |
| author_facet | Ito, Hiroyuki Takayashiki, Shota |
| contents | As a generalization of a quasi-elliptic surface, there is a quasi-hyperelliptic surface, a nonsingular projective surface which has a fibration structure whose general fiber is a quasi-hyperelliptic curve ($=$ singular hyperelliptic curve with one cuspidal singular point) of genus $(p-1)/2$ in characteristic $p \ge 5$. In this paper, we consider unirational quasi-hyperelliptic surfaces in characteristic $5$, and classify singular fibers and give a formula for the arithmetic genus and the self-intersection number of the canonical divisor. As a corollary, we classify rational quasi-hyperelliptic surfaces by determining the combinations of singular fibers, the defining equations and sections. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_17790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unirational quasi-hyperelliptic surfaces in characteristic five Ito, Hiroyuki Takayashiki, Shota Algebraic Geometry 14G17, 14D06, 11G30 As a generalization of a quasi-elliptic surface, there is a quasi-hyperelliptic surface, a nonsingular projective surface which has a fibration structure whose general fiber is a quasi-hyperelliptic curve ($=$ singular hyperelliptic curve with one cuspidal singular point) of genus $(p-1)/2$ in characteristic $p \ge 5$. In this paper, we consider unirational quasi-hyperelliptic surfaces in characteristic $5$, and classify singular fibers and give a formula for the arithmetic genus and the self-intersection number of the canonical divisor. As a corollary, we classify rational quasi-hyperelliptic surfaces by determining the combinations of singular fibers, the defining equations and sections. |
| title | Unirational quasi-hyperelliptic surfaces in characteristic five |
| topic | Algebraic Geometry 14G17, 14D06, 11G30 |
| url | https://arxiv.org/abs/2508.17790 |