PERIOD DIFFERENTIAL EQUATIONS FOR THE FAMILIES OF K3 SURFACES WITH TWO PARAMETERS DERIVED FROM THE REFLEXIVE POLYTOPES

抄録

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 projective monodromy 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).