Polytope duality for families of $K3$ surfaces associated to singularities $Q_{16}$ and $S_{16}$

TL;DR

This paper investigates the duality relationships of families of K3 surfaces linked to specific bimodal singularities, expanding understanding of their geometric and algebraic structures beyond invertible cases.

Contribution

It introduces a study of K3 surface families associated with non-invertible bimodal singularity pairs, highlighting their duality properties and geometric structures.

Findings

Identification of dual pairs of K3 surface families

Analysis of singularity types Q_{16} and S_{16}

Insights into non-invertible singularity dualities

Abstract

There are strange dual pairs of bimodal singularities that are not assigned an invertible projectivisation in EbelingPloog. We study families of $K3$ surfaces associated to such pairs.