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Abelian Varieties with Quaternion Multiplication

Ron Donagi·Ron Livné
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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.

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Ron Donagi, Ron Livné. 2005-12-02. Abelian Varieties with Quaternion Multiplication. https://arxiv.org/abs/math/0507493

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