Picard-Fuchs equations of families of QM abelian surfaces

2012/02/13 by Amnon Besser, Besser, Amnon, Ron Livné +1
Mathematics · #14D07 (Primary) 14J27 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14D07 #msc:14J27

paper · pdf · doi:10.48550/arxiv.1202.2808

AMS-LaTeX, algorithm2e style, ypic, 18 pages

arxiv created 2012/02/14 · arxiv updated 2012/02/15

Abstract

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.

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