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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.14512 |
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| _version_ | 1866911963478491136 |
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| author | Orlić, Petar |
| author_facet | Orlić, Petar |
| contents | For every group $\{\pm1\}\subseteq Δ\subseteq (\mathbb{Z}/N\mathbb{Z})^\times$, there exists an intermediate modular curve $X_Δ(N)$. In this paper we determine all curves $X_Δ(N)$ whose $\mathbb{Q}$-gonality is equal to $4$, all curves $X_Δ(N)$ whose $\mathbb{C}$-gonality is equal to $4$, and all curves $X_Δ(N)$ whose $\mathbb{Q}$-gonality is equal to $5$. We also determine the $\mathbb{Q}$-gonality of all curves $X_Δ(N)$ for $N\leq 40$ and $\{\pm1\}\subsetneq Δ\subsetneq (\mathbb{Z}/N\mathbb{Z})^\times$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tetragonal intermediate modular curves Orlić, Petar Number Theory For every group $\{\pm1\}\subseteq Δ\subseteq (\mathbb{Z}/N\mathbb{Z})^\times$, there exists an intermediate modular curve $X_Δ(N)$. In this paper we determine all curves $X_Δ(N)$ whose $\mathbb{Q}$-gonality is equal to $4$, all curves $X_Δ(N)$ whose $\mathbb{C}$-gonality is equal to $4$, and all curves $X_Δ(N)$ whose $\mathbb{Q}$-gonality is equal to $5$. We also determine the $\mathbb{Q}$-gonality of all curves $X_Δ(N)$ for $N\leq 40$ and $\{\pm1\}\subsetneq Δ\subsetneq (\mathbb{Z}/N\mathbb{Z})^\times$. |
| title | Tetragonal intermediate modular curves |
| topic | Number Theory |
| url | https://arxiv.org/abs/2407.14512 |