%0 Journal Article
%A Etayo Gordejuela, José Javier
%A Martínez García, Ernesto
%T Fuchsian groups generated by half-turns and geometrical characterization of hyperelliptic and symmetric Riemann surfaces
%D 2004
%@ 0025-5521
%U https://hdl.handle.net/20.500.14352/50028
%X 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.
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