Communications in Number Theory and Physics
Volume 12 (2018)
Picard–Fuchs equations of families of QM abelian surfaces
Pages: 829 – 856
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 equations for several examples, which come from families of Kummer surfaces over Shimura curves, as studied in our previous work. We use this to find correspondences between the parameter spaces of our families and Shimura curves.
Received 20 December 2015
Accepted 2 August 2018
Published 14 January 2019