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Fuchsian groups generated by half-turns and geometrical characterization of hyperelliptic and symmetric Riemann surfaces

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Etayo Gordejuela, J. Javier and Martínez García, Ernesto (2004) Fuchsian groups generated by half-turns and geometrical characterization of hyperelliptic and symmetric Riemann surfaces. Mathematica Scandinavica, 95 (2). pp. 226-244. ISSN 0025-5521



Abstract

We construct a special type of fundamental regions for any Fuchsian group $F$ generated, by an even number of half-turns, and for certain non-Euclidean crystallographic groups (NEC groups in short). By comparing these regions we give geometrical conditions for F to be the canonical Fuchsian subgroup of one of those NEC groups. Precisely speaking, we deal with NEC groups of algebraic genus 0 having all periods in the signature equal to 2. By means of these conditions we give a characterization of hyperelliptic and symmetric Riemann surfaces.


Item Type:Article
Uncontrolled Keywords:Fuchsian groups and automorphic functions; Fuchsian groups and their generalizations
Subjects:Sciences > Mathematics > Group Theory
ID Code:15787
Deposited On:27 Jun 2012 11:31
Last Modified:27 Jun 2012 11:31

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