论文标题
低属的三角模块曲线
Triangular modular curves of low genus
论文作者
论文摘要
三角模块化曲线是模块化曲线的概括，这些曲线是由双曲三角基团的一致性亚组源于上半平面的商。这些曲线也自然而然地是带有monodromy $ \ text {pgl} _2（\ mathbb {f} _q）$或$ \ text {psl} _2（\ mathbb {f} _q）$的belyi映射来源。我们提出了一种计算方法，以列举低属的Borel型三角形模块化曲线，并进行此列举以质量水平和小属。
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 $\text{PGL}_2(\mathbb{F}_q)$ or $\text{PSL}_2(\mathbb{F}_q)$. 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.
