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

Ki Ichiro Hashimoto, Naoki Murabayashi

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)271-296
Number of pages26
JournalTohoku Mathematical Journal
Volume47
Issue number2
DOIs
Publication statusPublished - 1995 Jun

ASJC Scopus subject areas

  • Mathematics(all)

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