Strange duality between hypersurface and complete intersection singularities

TL;DR

This paper explores a duality between hypersurface and complete intersection singularities, linking it to mirror symmetry and Berglund-H"ubsch transposition, extending Arnold's original strange duality.

Contribution

It derives a new duality between singularity types from mirror symmetry and invertible polynomial transposition, expanding the understanding of singularity classifications.

Findings

Establishes a duality connecting hypersurface and complete intersection singularities.

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

Extends Arnold's strange duality to broader classes of singularities.

Abstract

C.T.C. Wall and the first author discovered an extension of Arnold's strange duality embracing on one hand series of bimodal hypersurface singularities and on the other, isolated complete intersection singularities. In this paper, we derive this duality from the mirror symmetry and the Berglund-H\"ubsch transposition of invertible polynomials.