Period differential equations for families of K3 surfaces derived from some 3 dimensional reflexive polytopes

Abstract

We study period maps for families of $K3$ surfaces those are given by anti canonical divisors of toric varieties coming from reflexive polytopes $P_2,P_4,P_5$ and $P_r$. We obtain systems of period differential equations for these families. Moreover, in the case $P_4$, we determine the projective monodromy group of the period map. This group is explicitly related with the Hilbert modular group for $\mathbb{Q}(\sqrt{5})$.

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)

• Computing Differential Equations for Integrals Associated to Smooth Fano Polytopes