| On q-n-gonal Klein Surfaces |
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| 作者姓名： | B. ESTRADA R. A. HIDALGO E. MARTINEZ |
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| 作者单位： | [1]Departamento de Matemdticas Fundamentales, UNED, Paseo Senda del Rey 9, 28040 Madrid, Spain [2]Departamento de Matemdtica, Universidad Tdcnica Federico Santa Maria, Casilla 110- V Valparaiso, Chile |
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| 基金项目： | The first and third authors are partially supported by Project MTM2005-01637; the second is partially supported by Projects Fondecyt 1030252, 1030373 and UTFSM 12.05.21 |
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| 摘 要： | We consider proper Klein surfaces X of algebraic genus p ≥ 2, having an automorphism φ of prime order n with quotient space X/（φ） of algebraic genus q. These Klein surfaces axe called q-n-gonal surfaces and they are n-sheeted covers of surfaces of algebraic genus q. In this paper we extend the results of the already studied cases n ≤ 3 to this more general situation. Given p ≥ 2, we obtain, for each prime n, the （admissible） values q for which there exists a q-n-gonal surface of algebraic genus p. Furthermore, for each p and for each admissible q, it is possible to check all topological types of q-n-gonal surfaces with algebraic genus p. Several examples are given： q-pentagonal surfaces and q-n-gonal bordered surfaces with topological genus g = 0, 1.
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| 关 键 词： | Klein表面 黎曼表面 自同构群 欧几里德群 |
| 收稿时间： | 25 May 2005 |
| 修稿时间： | 2005-05-25 |
On q-n-gonal Klein Surfaces |
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| B. ESTRADA R. A. HIDALGO E. MARTINEZ.On q-n-gonal Klein Surfaces[J].Acta Mathematica Sinica,2007,23(10):1833-1844. |
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| Authors: | B Estrada R A Hidalgo E Martínez |
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| Institution: | (1) Departamento de Matemáticas Fundamentales, UNED, Paseo Senda del Rey 9, 28040 Madrid, Spain;(2) Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaiso, Chile;(3) Departamento de Matemáticas Fundamentales, UNED, Paseo Senda del Rey 9, 28040 Madrid, Spain |
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| Abstract: | We consider proper Klein surfaces X of algebraic genus p ≥ 2, having an automorphism ϕ of prime order n with quotient space X/〈ϕ〉 of algebraic genus q. These Klein surfaces are called q-n-gonal surfaces and they are n-sheeted covers of surfaces of algebraic genus q. In this paper we extend the results of the already studied cases n ≤ 3 to this more general situation. Given p ≥ 2, we obtain, for each prime n, the (admissible) values q for which there exists a q-n-gonal surface of algebraic genus p. Furthermore, for each p and for each admissible q, it is possible to check all topological types of q-n-gonal surfaces with algebraic genus p. Several examples are given: q-pentagonal surfaces and q-n-gonal bordered surfaces with topological genus g = 0, 1.
The first and third authors are partially supported by Project MTM2005–01637; the second is partially supported by Projects
Fondecyt 1030252, 1030373 and UTFSM 12.05.21 |
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| Keywords: | Klein surfaces Riemann surfaces automorphism groups non-Euclidean crystallographic groups |
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