Triangular modular curves of low genus
Juanita Duque-Rosero, John Voight

TL;DR
This paper introduces a computational method to enumerate low-genus triangular modular curves, which generalize classical modular curves and are linked to Belyi maps with specific monodromy groups.
Contribution
The paper develops a new computational approach to classify low-genus triangular modular curves at prime levels, expanding understanding of their structure and properties.
Findings
Enumeration of Borel-type triangular modular curves for small genus
Identification of curves with specific monodromy groups
Extension of classification methods for modular curves
Abstract
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 or . 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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Advanced Algebra and Geometry
