Triangular modular curves of small genus

被引：0
作者：
Juanita Duque-Rosero
John Voight
机构：
[1] Dartmouth College,Department of Mathematics
来源：
Research in Number Theory | 2023年 / 9卷
关键词：
Triangle groups; Modular curves; Congruence subgroups; Belyi maps;
D O I：
暂无
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学科分类号：
摘要：
Triangular modular curves are a generalization of modular curves that arise from quotients of the upper half-plane by congruence subgroups of hyperbolic triangle groups. These curves also arise naturally as a source of Belyi maps with monodromy PGL2(Fq)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {PGL}_2(\mathbb {F}_q)$$\end{document} or PSL2(Fq)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {PSL}_2(\mathbb {F}_q)$$\end{document}. We present a computational approach to enumerate Borel-type triangular modular curves of low genus, and we carry out this enumeration for prime level and small genus.
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