Elliptic fibrations of K3 surfaces and QM kummer surfaces

Math. Zeitschrift 228 (1998), No. 2, 283--308 get the paper from Math. Zeitschrift

Abstract: We compute equations for the universal family of Kummer surfaces over Shimura curves associated to rational quaternion algebras for a few small discriminants. We apply 2 different methods. The first relies on a computation of the cohomology of a QM Abelian surface to get an elliptic fibrations of the associated Kummer surface. The second methods identifies the image of the Shimura curve in a Siegel 3--fold as the intersection of 2 Humbert surfaces.

On the equations defining families of Kummer surfaces of quaternionic multiplication type

qmkummer.dvi.gz (65k) Note: if you would like to print this paper, after downloading it into your machine, gunzip it by giving the command "gunzip qmkummer.dvi".

Abstract: This is an older and longer version of the same paper which is essentially part of my Ph.D. Thesis. There are some errors in this version that have hopefully been corrected in the new version. Also, the new version is shorter. On the other hand, the old version has more details, some expository and some that may be of interest and will hopefully be expanded on in future publications.

There are a few encapsulated postcript figures. To see them you will have to transfer to your local machine some figures to be found here