Minimal regular normal crossings models of superelliptic curves
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911030018310144 |
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| author | Obus, Andrew Srinivasan, Padmavathi |
| author_facet | Obus, Andrew Srinivasan, Padmavathi |
| contents | Let $K$ be a complete discretely valued field with perfect residue field $k$. If $X \to \mathbb{P}^1_K$ is a $\mathbb{Z}/d$-cover with $\text{char } k \nmid d$, we compute the minimal regular normal crossings model $\mathcal{X}$ of $X$ as the normalization of an explicit normal model $\mathcal{Y}$ of $\mathbb{P}^1_K$ in $K(X)$. The model $\mathcal{Y}$ is given using Mac Lane's description of discrete valuations on the rational function field $K(\mathbb{P}^1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_24091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal regular normal crossings models of superelliptic curves Obus, Andrew Srinivasan, Padmavathi Algebraic Geometry Primary: 14B05, 14J17 Secondary: 13F30, 14H25 Let $K$ be a complete discretely valued field with perfect residue field $k$. If $X \to \mathbb{P}^1_K$ is a $\mathbb{Z}/d$-cover with $\text{char } k \nmid d$, we compute the minimal regular normal crossings model $\mathcal{X}$ of $X$ as the normalization of an explicit normal model $\mathcal{Y}$ of $\mathbb{P}^1_K$ in $K(X)$. The model $\mathcal{Y}$ is given using Mac Lane's description of discrete valuations on the rational function field $K(\mathbb{P}^1)$. |
| title | Minimal regular normal crossings models of superelliptic curves |
| topic | Algebraic Geometry Primary: 14B05, 14J17 Secondary: 13F30, 14H25 |
| url | https://arxiv.org/abs/2506.24091 |