Abelian Varieties with Quaternion Multiplication
Algebraic Geometry
2007-05-23 v3
Abstract
In this article we use a Prym construction to study low dimensional abelian varieties with an action of the quaternion group. In special cases we describe the Shimura variety parameterizing such abelian varieties, as well as a map to this Shimura variety from a natural parameter space of quaternionic abelian varieties. Our description is based on the moduli of cubic threefolds with nine nodes, which we study in some detail.
Cite
@article{arxiv.math/0507493,
title = {Abelian Varieties with Quaternion Multiplication},
author = {Ron Donagi and Ron Livné},
journal= {arXiv preprint arXiv:math/0507493},
year = {2007}
}
Comments
34 pages. An appendix added for the new version