Quasi-abelian group as automorphism group of Riemann surfaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913092145774592 |
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| author | Hidalgo, Rubén A. Montilla, Yerika Marín Quispe, Saúl |
| author_facet | Hidalgo, Rubén A. Montilla, Yerika Marín Quispe, Saúl |
| contents | Conformal/anticonformal actions of the quasi-abelian group $QA_{n}$ of order $2^n$, for $n\geq 4$, on closed Riemann surfaces, pseudo-real Riemann surfaces and closed Klein surfaces are considered. We obtain several consequences, such as the solution of the minimum genus problem for the $QA_n$-actions, and for each of these actions, we study the topological rigidity action problem. In the case of pseudo-real surfaces, attention was typically restricted to group actions that admit anticonformal elements. In this paper we consider two cases: either $QA_n$ has anticonformal elements or only contains conformal elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_05468 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quasi-abelian group as automorphism group of Riemann surfaces Hidalgo, Rubén A. Montilla, Yerika Marín Quispe, Saúl Algebraic Geometry Conformal/anticonformal actions of the quasi-abelian group $QA_{n}$ of order $2^n$, for $n\geq 4$, on closed Riemann surfaces, pseudo-real Riemann surfaces and closed Klein surfaces are considered. We obtain several consequences, such as the solution of the minimum genus problem for the $QA_n$-actions, and for each of these actions, we study the topological rigidity action problem. In the case of pseudo-real surfaces, attention was typically restricted to group actions that admit anticonformal elements. In this paper we consider two cases: either $QA_n$ has anticonformal elements or only contains conformal elements. |
| title | Quasi-abelian group as automorphism group of Riemann surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2303.05468 |