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Automorphism groups of hyperelliptic Riemann surfaces

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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

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


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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
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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