Relationship between two Calabi–Yau orbifolds arising as hyper–surfaces in a quotient of the same weighted projective space

Abstract

In this article we consider a question: what is the relation between two Calabi-Yau manifolds of two different Berglund–Hubsch types if they appear as hyper–surfaces in the quotient of the same weighted projective space. We show that these manifolds are connected by a special change of coordinates, which we call the resonance transformation.