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Bujalance, E. and Etayo Gordejuela, J. Javier
(1987)
*Automorphism groups of hyperelliptic Riemann surfaces.*
Kodai Mathematical Journal, 10
(2).
pp. 174-181.
ISSN 0386-5991

PDF
Restringido a Repository staff only 604kB |

Official URL: http://projecteuclid.org/euclid.kmj/1138037412

## Abstract

If G is a group of automorphisms of a hyperelliptic Riemann surface of genus g represented as D/$\Gamma$ where D is the hyperbolic plane and $\Gamma$ a Fuchsian group, then $G\cong \Gamma '/\Gamma$ where $\Gamma$ ' is also a Fuchsian group. Furthermore G contains a central subgroup $G\sb 1$ of order 2 and if $\Gamma\sb 1$ is the corresponding subgroup of $\Gamma$ ', then $G/G\sb 1$ is a group of automorphisms of the sphere $D/\Gamma\sb 1$. Using this and structure theorem for Fuchsian groups the authors determine all surfaces of genus $g>3$ admitting groups G with $o(G)>8(g-1)$. There are two infinite families both corresponding to $\Gamma$ ' being the triangle group (2,4,m) and six other groups.

Item Type: | Article |
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Uncontrolled Keywords: | Classification theory of Riemann surfaces; Coverings, fundamental group; Special curves and curves of low genus |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 15765 |

Deposited On: | 26 Jun 2012 10:34 |

Last Modified: | 07 Aug 2018 07:23 |

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