Shimura curves as intersections of Humbert surfaces and defining equations of QM-curves of genus two (Q1897783)
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scientific article; zbMATH DE number 794318
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Shimura curves as intersections of Humbert surfaces and defining equations of QM-curves of genus two |
scientific article; zbMATH DE number 794318 |
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Shimura curves as intersections of Humbert surfaces and defining equations of QM-curves of genus two (English)
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10 September 1995
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A QM-curve is a curve of genus two whose Jacobian variety is an abelian surface with quaternion multiplication. In this paper, the authors consider fiber varieties over a Shimura curve whose fibers are QM-curves. They give an explicit defining equation for such a fiber variety when the discriminant of the associated quaternion algebra is six or ten.
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Humbert surfaces
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QM-curve
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fiber varieties
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Shimura curve
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quaternion algebra
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