Bounds on the orders of groups of automorphisms of a pseudo-real surface of given genus
A compact Riemann surface is called pseudo-real if it admits anti-conformal (orientationreversing) automorphisms, but no anti-conformal automorphism of order 2. In this paper, we consider upper bounds on the order of a group G of automorphisms of a pseudo-real surface S of given genus g > 1, in g...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad Nacional de Educación a Distancia |
| Repositorio: | e-spacio. Repositorio Institucional de la UNED |
| Idioma: | inglés |
| OAI Identifier: | oai:e-spacio.uned.es:20.500.14468/31244 |
| Acceso en línea: | https://hdl.handle.net/20.500.14468/31244 |
| Access Level: | acceso abierto |
| Palabra clave: | 1204 Geometría 30F10 (primary) 14F37 20B25 20H10 (secondary) |
| Sumario: | A compact Riemann surface is called pseudo-real if it admits anti-conformal (orientationreversing) automorphisms, but no anti-conformal automorphism of order 2. In this paper, we consider upper bounds on the order of a group G of automorphisms of a pseudo-real surface S of given genus g > 1, in general and for certain special cases. We determine for all g 2 the orders of the largest cyclic group and the largest abelian group of automorphisms of a pseudo-real surface of genus g, containing orientation-reversing elements, and consider the problem of finding similar bounds when the group contains no orientation-reversing elements. For arbitrary groups, we show that if M(g) is the order of the largest group of automorphisms of a pseudo-real surface of genus g, then M(g) 2g for every even g 2, while M(g) 4(g − 1) for every odd g 3, and we prove that the latter bound is sharp for a very large and possibly infinite set of odd values of g 3. We also give the precise values of M(g) for all g between 2 and 128, together with the signatures for the actions of the corresponding groups of largest order. |
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