Multiply Quasiplatonic Riemann Surfaces
Multiply Quasiplatonic Riemann Surfaces
复制标题
乘以准柏拉图黎曼曲面
DOI：
10.1080/10586458.2003.10504514
复制
发表时间：
2003
影响因子：
0.5
通讯作者：
E. Girondo
中科院分区：
文献类型：
--
作者：
E. Girondo
本文的目的是研究一个紧致黎曼曲面可能包含两个不同类型的正则dessin d'enfants的情况。根据Fuchsian群，一个等价条件是一致化群通常包含在几个不同的三角形群中。这个问题以图形理论的方式得到解答，提供了算法来决定携带规则dessin（准柏拉图式表面）的表面是否也可以携带其他规则dessin。然后根据其算术性质研究了乘拟柏拉图曲面。最后计算了含有大量非算术正则设计的最低亏格曲面。
The aim of this article is the study of the circumstances under which a compact Riemann surface may contain two regular dessin d'enfants of different types. In terms of Fuchsian groups, an equivalent condition is the uniformizing group being normally contained in several different triangle groups. The question is answered in a graph-theoretical way, providing algorithms that decide if a surface that carries a regular dessin (a quasiplatonic surface) can also carry other regular dessins. The multiply quasiplatonic surfaces are then studied depending on their arithmetic character. Finally, the surfaces of lowest genus carrying a large number of nonarithmetic regular dessins are computed.