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

Atsuhira Nagano

    Research output: Contribution to journal › Article

    4 Citations (Scopus)

    Abstract

    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
    Volume66
    Issue number1
    DOIs
    Publication statusPublished - 2012

    Fingerprint

    K3 Surfaces
    Polytopes
    Two Parameters
    Differential equation
    Lattice Structure
    Orbifold
    Hilbert
    Three-dimensional
    Family

    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Period differential equations for the families of K3 surfaces with two parameters derived from the reflexive polytopes. / Nagano, Atsuhira.

    In: Kyushu Journal of Mathematics, Vol. 66, No. 1, 2012, p. 193-244.

    Research output: Contribution to journal › Article

    Nagano, A 2012, 'Period differential equations for the families of K3 surfaces with two parameters derived from the reflexive polytopes', Kyushu Journal of Mathematics, vol. 66, no. 1, pp. 193-244. https://doi.org/10.2206/kyushujm.66.193
    Nagano A. Period differential equations for the families of K3 surfaces with two parameters derived from the reflexive polytopes. Kyushu Journal of Mathematics. 2012;66(1):193-244. https://doi.org/10.2206/kyushujm.66.193
    Nagano, Atsuhira. / Period differential equations for the families of K3 surfaces with two parameters derived from the reflexive polytopes. In: Kyushu Journal of Mathematics. 2012 ; Vol. 66, No. 1. pp. 193-244.
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