We describe an algorithm for computing the Picard-Fuchs equation for a family of twists of a fixed elliptic surface. We then apply this algorithm to obtain the equation for several examples, which are coming from families of Kummer surfaces over Shimura curves, as studied in our previous work. We use this to find correspondenced between the parameter spaces of our families and Shimura curves. These correspondences can sometimes be proved rigorously.

中文翻译：

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QM 阿贝尔曲面族的 Picard-Fuchs 方程

我们描述了一种用于计算固定椭圆表面扭曲族的 Picard-Fuchs 方程的算法。然后我们应用这个算法来获得几个例子的方程，这些例子来自 Shimura 曲线上的 Kummer 曲面族，正如我们之前的工作所研究的那样。我们用它来找到我们家庭的参数空间和 Shimura 曲线之间的对应关系。有时可以严格证明这些对应关系。