# A mirror duality for families of $K3$ surfaces associated to bimodular singularities

## TL;DR

This paper explores a lattice duality in families of K3 surfaces linked to bimodular singularities, extending known polytope mirror symmetry to a lattice-based symmetry, enriching the understanding of mirror symmetry in algebraic geometry.

## Contribution

It introduces a new lattice duality for K3 surface families associated with bimodular singularities, expanding the scope of mirror symmetry beyond polytopes.

## Key findings

- Establishes a lattice duality extending polytope mirror symmetry.
- Connects bimodular singularities with lattice symmetries in K3 surfaces.
- Enhances the theoretical framework of mirror symmetry in algebraic geometry.

## Abstract

Ebeling and Ploog \cite{EbelingPloog} studied a duality of bimodular singularities which is part of the Berglund--H$\ddot{\textnormal{u}}$bsch mirror symmetry. Mase and Ueda \cite{MU} showed that this duality leads to a polytope mirror symmetry of families of $K3$ surfaces. We discuss in this article how this symmetry extends to a symmetry between lattices.