2022/03/12 by Samuele Anni, Anni, Samuele, Eran Assaf +3 · 1 citation
Mathematics · #11F11 #11G18 #14G35 #14H45 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2203.06370
openalex publication_date 2022/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove that there are finitely many modular curves that admit a smooth plane model. Moreover, if the degree of the model is greater than or equal to 19, no such curve exists. For modular curves of Shimura type we show that none can admit a smooth plane model of degree 5, 6 or 7. Further, if a modular curve of Shimura type admits a smooth plane model of degree 8 we show that it must be a twist of one of four curves.