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

Etayo Gordejuela, José JavierMartínez García, Ernesto2023-06-202023-06-2020040025-5521https://hdl.handle.net/20.500.14352/50028We 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.Fuchsian groups generated by half-turns and geometrical characterization of hyperelliptic and symmetric Riemann surfacesjournal articlemetadata only access512.54Fuchsian groups and automorphic functionsFuchsian groups and their generalizationsGrupos (Matemáticas)