An unusual family of supersingular curves of genus five in characteristic two
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915748641767424 |
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| author | Dragutinović, Dušan |
| author_facet | Dragutinović, Dušan |
| contents | We construct a family of smooth supersingular curves of genus $5$ in characteristic $2$ with several notable features: its dimension matches the expected dimension of any component of the supersingular locus in genus $5$, its members are non-hyperelliptic curves with non-trivial automorphism groups, and each curve in the family admits a double cover structure over both an elliptic curve and a genus-$2$ curve. We also provide an explicit parametrization of this family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An unusual family of supersingular curves of genus five in characteristic two Dragutinović, Dušan Algebraic Geometry Number Theory We construct a family of smooth supersingular curves of genus $5$ in characteristic $2$ with several notable features: its dimension matches the expected dimension of any component of the supersingular locus in genus $5$, its members are non-hyperelliptic curves with non-trivial automorphism groups, and each curve in the family admits a double cover structure over both an elliptic curve and a genus-$2$ curve. We also provide an explicit parametrization of this family. |
| title | An unusual family of supersingular curves of genus five in characteristic two |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2507.03519 |