Galois lines for a canonical curve of genus 4, III: non-cyclic Galois lines
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913072786964480 |
|---|---|
| author | Kato, Shotaro Komeda, Jiryo Takahashi, Takeshi |
| author_facet | Kato, Shotaro Komeda, Jiryo Takahashi, Takeshi |
| contents | Let $C \subset \mathbb{P}^3$ be a canonical curve of genus $4$ over an algebraically closed field $k$ of characteristic zero. For a line $l \subset \mathbb{P}^3$, we consider the projection $π_l: C \to \mathbb{P}^1$ from $l$ and the induced extension of function fields $π_l^*: k(\mathbb{P}^1)\hookrightarrow k(C)$. A line $l$ is called an \emph{$S_3$-line} (resp. a \emph{$K_4$-line}) if the extension $k(C)/π_l^*(k(\mathbb{P}^1))$ is Galois and its Galois group is isomorphic to the symmetric group $S_3$ on three letters (resp. the Klein four-group $K_4$). We prove that the number of $S_3$-lines (resp.\ $K_4$-lines) is at most $10$ (resp.\ $15$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26584 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Galois lines for a canonical curve of genus 4, III: non-cyclic Galois lines Kato, Shotaro Komeda, Jiryo Takahashi, Takeshi Algebraic Geometry Primary: 14H50, Secondary: 14H37, 14H45 Let $C \subset \mathbb{P}^3$ be a canonical curve of genus $4$ over an algebraically closed field $k$ of characteristic zero. For a line $l \subset \mathbb{P}^3$, we consider the projection $π_l: C \to \mathbb{P}^1$ from $l$ and the induced extension of function fields $π_l^*: k(\mathbb{P}^1)\hookrightarrow k(C)$. A line $l$ is called an \emph{$S_3$-line} (resp. a \emph{$K_4$-line}) if the extension $k(C)/π_l^*(k(\mathbb{P}^1))$ is Galois and its Galois group is isomorphic to the symmetric group $S_3$ on three letters (resp. the Klein four-group $K_4$). We prove that the number of $S_3$-lines (resp.\ $K_4$-lines) is at most $10$ (resp.\ $15$). |
| title | Galois lines for a canonical curve of genus 4, III: non-cyclic Galois lines |
| topic | Algebraic Geometry Primary: 14H50, Secondary: 14H37, 14H45 |
| url | https://arxiv.org/abs/2604.26584 |