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

Kiichiro Hashimoto, Naoki Murabayashi

    Research output: Contribution to journalArticle

    31 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

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    Abelian Surfaces
    Genus
    Intersection
    Fiber
    Curve
    Jacobian Varieties
    Quaternion Algebra
    Isomorphism Classes
    Quaternion
    Discriminant
    Multiplication
    Classify

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Shimura curves as intersections of humbert surfaces and defining equations of QM-curves of genus two. / Hashimoto, Kiichiro; Murabayashi, Naoki.

    In: Tohoku Mathematical Journal, Vol. 47, No. 2, 1995, p. 271-296.

    Research output: Contribution to journalArticle

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