On smooth plane models for modular curves of Shimura type
Number Theory
2022-09-26 v3 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2203.06370,
title = {On smooth plane models for modular curves of Shimura type},
author = {Samuele Anni and Eran Assaf and Elisa Lorenzo García},
journal= {arXiv preprint arXiv:2203.06370},
year = {2022}
}