Dessins on Modular Curves

2016/03/05 by Khashayar Filom, Filom, Khashayar, Ali Kamalinejad +1 · 1 citation
Mathematics · #11F03 #14H57 #14Q05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1603.01693

openalex publication_date 2016/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a finite index subgroup Γ of \rmPSL₂(ℤ), we investigate Belyi functions on the corresponding modular curve X(Γ) by introducing two methods for constructing such functions. Numerous examples have been worked out completely and as an application, we have derived modular equations for Γ₀(2),Γ₀(3) and several special values of the j-function by a new method based on the theory of Belyi functions and dessin d'enfants.

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• Moduli of elliptic K3 surfaces: monodromy and Shimada root lattice strata

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