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

Authors

  • J. J. Etayo
  • E. Martínez

DOI:

https://doi.org/10.7146/math.scand.a-14457

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 in order to $F$ 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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Published

2004-12-01

How to Cite

Etayo, J. J., & Martínez, E. (2004). Fuchsian groups generated by half-turns and geometrical characterization of hyperelliptic and symmetric Riemann surfaces. MATHEMATICA SCANDINAVICA, 95(2), 226–244. https://doi.org/10.7146/math.scand.a-14457

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Articles