Fuchsian groups generated by half-turns and geometrical characterization of hyperelliptic and symmetric Riemann surfaces
Fuchsian groups generated by half-turns and geometrical characterization of hyperelliptic and symmetric Riemann surfaces
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由半圈生成的福克斯群以及超椭圆和对称黎曼曲面的几何表征
DOI：
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发表时间：
2004
期刊：
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通讯作者：
E. Martínez
中科院分区：
文献类型：
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作者：
J. Etayo;E. Martínez
我们构造了一种特殊类型的基本区域的任何Fuchsian群$F$生成的偶数个半圈，并为某些非欧几里德晶体群（NEC集团简称）。通过比较这些地区，我们给几何条件，以$F$是典型的Fuchsian子群的NEC集团之一。准确地说，我们处理NEC群的代数亏格$0$有所有期间的签名等于$2$。利用这些条件，我们给出了超椭圆对称黎曼曲面的一个刻划。
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.