论文标题
在平滑的平面模型上，用于模块化的shimura类型
On smooth plane models for modular curves of Shimura type
论文作者
论文摘要
在本文中，我们证明有许多模块化曲线可以接收平滑的平面模型。此外，如果模型的程度大于或等于19，则不存在这样的曲线。对于Shimura型的模块化曲线，我们表明没有一个人可以接受5度，6或7度的平滑平面模型。此外，如果Shimura类型的模块化曲线承认8度8的平滑平面模型，我们表明它必须是四个曲线之一的扭曲。
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.
