A period differential equation for a family of $K3$ surfaces and the Hilbert modular orbifold for the field $\mathbb{Q}(\sqrt{5})$

Abstract

In this article we study the period map for a family of $K3$ surfaces which is given by the anticanonial divisor of a toric variety. We determine the period differential equation and its monodromy group. Moreover we show the exact relation between our period differential equation and the unifomizing differential equation of the Hilbert modular orbifold for the field $\mathbb{Q}(\sqrt{5})$.

The results of this paper are contained in "Period differential equations for the families of K3 surfaces with 2 parameters derived from the reflexive polytopes "

References in corpus (1)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties

Cited by in corpus (1)

• Period differential equations for families of $K3$ surfaces derived from 3 dimensional reflexive polytopes with 5 vertices