Shimura curves as intersections of Humbert surfaces and defining equations of QM-curves of genus two

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概要

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• Shimura curves classify isomorphism classes of abelian surfaces with quaternion multiplication. In this paper, we are concerned with a fibre space, the base space of which is a Shimura curve and fibres are curves of genus two whose jacobian varieties are abelian surfaces of the above type. We shall give an explicit defining equation for such a fibre space when the discriminant of the quaternion algebra is 6 or 10.

• 東北大学の論文

著者

• Murabayashi Naoki

  Department Of Mathematics Faculty Of Science Yamagata University

• Hashimoto Ki-ichiro

  Department of Mathematics, School of Science and Engineering, Waseda University

• Hashimoto Ki-ichiro

  Department Of Mathematics School Of Science And Engineering Waseda University

関連論文

• Shimura curves as intersections of Humbert surfaces and defining equations of QM-curves of genus two
• Class numbers of definite unimodular Hermitian forms over the rings of imaginary quadratic fields
• Class numbers of positive definite binary and ternary unimodular Hermitian forms

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