Shimura curves as intersections of Humbert surfaces and defining equations of QM-curves of genus two
type: Item
instance of: scholarly article
title: Shimura curves as intersections of Humbert surfaces and defining equations of QM-curves of genus two
zbMATH Open document ID: 0838.11044
author: Naoki Murabayashi
author: Ki-ichiro Hashimoto
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1995-09-10T00:00:00Z
review text: 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.
reviewed by: Min Ho Lee
Mathematics Subject Classification ID: 11G15
Mathematics Subject Classification ID: 11G18
Mathematics Subject Classification ID: 14G35
Mathematics Subject Classification ID: 14H40
zbMATH DE Number: 794318
zbMATH Keywords: Humbert surfaces
zbMATH Keywords: QM-curve
zbMATH Keywords: fiber varieties
zbMATH Keywords: Shimura curve
zbMATH Keywords: quaternion algebra
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225596
OpenAlex ID: W2168213702
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DOI: 10.2748/TMJ/1178225596
description: scientific article; zbMATH DE number 794318