Computing the Stable Reduction of Hyperelliptic Curves in Residue Characteristic 2
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912447148851200 |
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| author | Gehrunger, Tim |
| author_facet | Gehrunger, Tim |
| contents | Consider a hyperelliptic curve of genus $g$ over a field $K$ of characteristic zero. After extending $K$ we can view it as a marked curve with its $2g+2$ Weierstrass points. We prove some general properties of the stable reduction of this marked curve for a valuation of residue characteristic $2$ and refine an existing algorithm for its computation. We work out explicit examples up to genus $g=30$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19663 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computing the Stable Reduction of Hyperelliptic Curves in Residue Characteristic 2 Gehrunger, Tim Algebraic Geometry Number Theory 14H30 (14H10, 11G20) Consider a hyperelliptic curve of genus $g$ over a field $K$ of characteristic zero. After extending $K$ we can view it as a marked curve with its $2g+2$ Weierstrass points. We prove some general properties of the stable reduction of this marked curve for a valuation of residue characteristic $2$ and refine an existing algorithm for its computation. We work out explicit examples up to genus $g=30$. |
| title | Computing the Stable Reduction of Hyperelliptic Curves in Residue Characteristic 2 |
| topic | Algebraic Geometry Number Theory 14H30 (14H10, 11G20) |
| url | https://arxiv.org/abs/2506.19663 |