# Orbifold Jacobian algebras for exceptional unimodal singularities

## TL;DR

This paper demonstrates that orbifold Jacobian algebras for exceptional unimodal singularities are isomorphic to Jacobian algebras of Berglund-Hübsch transforms of dual singularities, revealing a deep duality structure.

## Contribution

It establishes a precise isomorphism between orbifold Jacobian algebras and Jacobian algebras of dual polynomials for exceptional unimodal singularities.

## Key findings

- Orbifold Jacobian algebras are isomorphic to Jacobian algebras of Berglund-Hübsch transforms.
- The duality between singularities is reflected in algebraic structures.
- This links singularity theory with mirror symmetry concepts.

## Abstract

This note shows that the orbifold Jacobian algebra associated to each invertible polynomial defining an exceptional unimodal singularity is isomorphic to the (usual) Jacobian algebra of the Berglund-H\"{u}bsch transform of an invertible polynomial defining the strange dual singularity in the sense of Arnold.