Strange duality between the quadrangle complete intersection singularities

TL;DR

This paper explores a mysterious duality between certain quadrangle complete intersection singularities, linking it to mirror symmetry, Berglund-H"ubsch transposition, and previous dualities in singularity theory.

Contribution

It introduces a new duality for quadrangle complete intersection singularities derived from mirror symmetry and matrix factorizations, expanding the understanding of singularity dualities.

Findings

Establishes a duality between quadrangle complete intersection singularities.

Connects the duality to mirror symmetry and Berglund-H"ubsch transposition.

Builds on previous results about hypersurface and complete intersection singularities.

Abstract

There is a strange duality between the quadrangle isolated complete intersection singularities discovered by the first author and C.T.C.Wall. We derive this duality from the mirror symmetry, the Berglund-H\"ubsch transposition of invertible polynomials, and our previous results about the strange duality between hypersurface and complete intersection singularities using matrix factorizations of size two.