Models and Integral Differentials of Hyperelliptic Curves
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866909394948587520 |
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| author | Muselli, Simone |
| author_facet | Muselli, Simone |
| contents | Let $C: y^2=f(x)$ be a hyperelliptic curve of genus $g\geq 1$, defined over a complete discretely valued field $K$, with ring of integers $O_K$. Under certain conditions on $C$, mild when residue characteristic is not $2$, we explicitly construct the minimal regular model with normal crossings $\mathcal{C}/O_K$ of $C$. In the same setting we determine a basis of integral differentials of $C$, that is an $O_K$-basis for the global sections of the relative dualising sheaf $ω_{\mathcal{C}/O_K}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_01830 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Models and Integral Differentials of Hyperelliptic Curves Muselli, Simone Number Theory Algebraic Geometry 11G20 (Primary) 14H45, 14F10 (Secondary) Let $C: y^2=f(x)$ be a hyperelliptic curve of genus $g\geq 1$, defined over a complete discretely valued field $K$, with ring of integers $O_K$. Under certain conditions on $C$, mild when residue characteristic is not $2$, we explicitly construct the minimal regular model with normal crossings $\mathcal{C}/O_K$ of $C$. In the same setting we determine a basis of integral differentials of $C$, that is an $O_K$-basis for the global sections of the relative dualising sheaf $ω_{\mathcal{C}/O_K}$. |
| title | Models and Integral Differentials of Hyperelliptic Curves |
| topic | Number Theory Algebraic Geometry 11G20 (Primary) 14H45, 14F10 (Secondary) |
| url | https://arxiv.org/abs/2003.01830 |