Author:
Anni Samuele,Assaf Eran,Lorenzo García Elisa
Abstract
AbstractIn 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.
Funder
Agence Nationale de la Recherche
Simons Foundation
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
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