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

TL;DR

This paper investigates families of K3 surfaces derived from specific 3D reflexive polytopes, analyzing their lattice structures, period differential equations, and monodromy groups to deepen understanding of their geometric properties.

Contribution

It provides a detailed study of K3 surface families from 3D reflexive polytopes with 5 vertices, including their lattice structures and monodromy groups, which is a novel analysis.

Findings

Determined lattice structures of the K3 families.

Derived period differential equations for these families.

Identified projective monodromy groups associated with the families.

Abstract

In this article we study the families of $K3$ surfaces derived from 3 dimensional 5 verticed reflexive polytopes with at most terminal singularity. We determine the lattice structures, the period differential equations and the projective monodromy groups for these families.