通过Neron-Severi的K3表面计算的Shimura曲线至少排名19
Shimura curve computations via K3 surfaces of Neron-Severi rank at least 19
摘要：
已知Picard数rho（= S的Neron-Severi群的秩）至少为19的K3曲面S由模曲线X参数化，并且这些模曲线X包括与Q上的四元数代数的同余子群相关联的各种Shimura模曲线。在一类这样的K3曲面中，一个曲面具有ρ =20当且仅当它对应于X上的CM点。我们使用它来计算Shimura曲线的方程，它们之间的自然映射，以及CM坐标，远远超出了我们在"Shimura Curve Computations“（1998）= <http://arxiv.org/abs/math/0005160>中直接使用曲线所能完成的工作。
英文摘要：
It is known that K3 surfaces S whose Picard number rho (= rank of the Neron-Severi group of S) is at least 19 are parametrized by modular curves X, and these modular curves X include various Shimura modular curves associated with congruence subgroups of quaternion algebras over Q. In a family of such K3 surfaces, a surface has rho=20 if and only if it corresponds to a CM point on X. We use this to compute equations for Shimura curves, natural maps between them, and CM coordinates well beyond what could be done by working with the curves directly as we did in ``Shimura Curve Computations'' (1998) = <http://arxiv.org/abs/math/0005160>
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