Period differential equations for the families of K3 surfaces with two parameters derived from the reflexive polytopes

Atsuhira Nagano

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    4 Citations (Scopus)


    In this paper, we study the period mappings for the families of K3 surfaces derived from the three-dimensional reflexive polytopes with five vertices. We determine the lattice structures, the period differential equations and the projectivemonodromy groups.Moreover, we show that one of our period differential equations coincides with the uniformizing differential equation of the Hilbert modular orbifold for the field ℚ(√5).

    Original languageEnglish
    Pages (from-to)193-244
    Number of pages52
    JournalKyushu Journal of Mathematics
    Issue number1
    Publication statusPublished - 2012



    • Hilbert modular orbifolds
    • K3 surfaces
    • Period differential equations
    • Period maps
    • Toric varieties

    ASJC Scopus subject areas

    • Mathematics(all)

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