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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2603.27431 |
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| _version_ | 1866910082247163904 |
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| author | Llerena-Córdova, Juan-Pablo |
| author_facet | Llerena-Córdova, Juan-Pablo |
| contents | Let $X$ be a compact Riemann surface of genus 2 and $D$ a very ample divisor with $ϕ_D$ its associated embedding into $\mathbb{P}^{n}$. We consider the set $G_{X,D}$ of linear subspaces $W$ of $\mathbb{P}^n$ of codimension $2$ with projection $π_W$ such that $f_W = π_W \circ ϕ_D$ is Galois, i.e. $f_W^*k(\mathbb{P}^1) \subseteq k(X)$ is a Galois extension. It is known that $G_{X,D}$ is isomorphic to a disjoint union of projective spaces. In this article, we calculate the dimension of projective spaces in the decomposition of $G_{X,D}$, when $D$ is induced by a subgroup of $\mathrm{Aut}(X)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27431 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Galois subspaces for compact Riemann surfaces of genus 2 Llerena-Córdova, Juan-Pablo Algebraic Geometry 14H37 Let $X$ be a compact Riemann surface of genus 2 and $D$ a very ample divisor with $ϕ_D$ its associated embedding into $\mathbb{P}^{n}$. We consider the set $G_{X,D}$ of linear subspaces $W$ of $\mathbb{P}^n$ of codimension $2$ with projection $π_W$ such that $f_W = π_W \circ ϕ_D$ is Galois, i.e. $f_W^*k(\mathbb{P}^1) \subseteq k(X)$ is a Galois extension. It is known that $G_{X,D}$ is isomorphic to a disjoint union of projective spaces. In this article, we calculate the dimension of projective spaces in the decomposition of $G_{X,D}$, when $D$ is induced by a subgroup of $\mathrm{Aut}(X)$. |
| title | Galois subspaces for compact Riemann surfaces of genus 2 |
| topic | Algebraic Geometry 14H37 |
| url | https://arxiv.org/abs/2603.27431 |