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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.19065 |
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| _version_ | 1866916017398087680 |
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| author | Liu, Qing |
| author_facet | Liu, Qing |
| contents | Let $C$ be a hyperelliptic curve of genus $g\ge 2$ over a discrete valuation field $K$ with perfect residue field. We study the minimal Weierstrass models of $C$. When there is more than one such model, we find interesting properties on the minimal regular model and the canonical model of $C$. For curves of genus $2$, we characterize the existence of the stable reduction in terms of the minimal Weierstrass models. When there is more than one such model, we can compute the Euler factor of $\mathrm{Jac}(C)$ and a volume form of the Néron model of $\mathrm{Jac}(C)$, using two specific minimal Weierstrass models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19065 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimal Weierstrass models and regular models of hyperelliptic curves Liu, Qing Number Theory 11G20, 14H25, 14G20 Let $C$ be a hyperelliptic curve of genus $g\ge 2$ over a discrete valuation field $K$ with perfect residue field. We study the minimal Weierstrass models of $C$. When there is more than one such model, we find interesting properties on the minimal regular model and the canonical model of $C$. For curves of genus $2$, we characterize the existence of the stable reduction in terms of the minimal Weierstrass models. When there is more than one such model, we can compute the Euler factor of $\mathrm{Jac}(C)$ and a volume form of the Néron model of $\mathrm{Jac}(C)$, using two specific minimal Weierstrass models. |
| title | Minimal Weierstrass models and regular models of hyperelliptic curves |
| topic | Number Theory 11G20, 14H25, 14G20 |
| url | https://arxiv.org/abs/2603.19065 |