On the equivalence of Batyrev and BHK Mirror symmetry constructions

Abstract

We consider the connection between two constructions of the mirror partner for the Calabi-Yau orbifold. This orbifold is defined as a quotient by some suitable subgroup $G$ of the phase symmetries of the hypersurface $X_M$ in the weighted projective space, cut out by a quasi-homogeneous polynomial $W_M$. The first, Berglund-Hübsch-Krawitz (BHK) construction, uses another weighted projective space and the quotient of a new hypersurface $X_{M^T}$ inside it by some dual group $G^T$. In the second, Batyrev construction, the mirror partner is constructed as a hypersurface in the toric variety defined by the reflexive polytope dual to the polytope associated with the original Calabi-Yau orbifold. We give a simple evidence of the equivalence of these two constructions.

References in corpus (2)

• FJRW rings and Landau-Ginzburg Mirror Symmetry
• JKLMR conjecture and Batyrev construction

Cited by in corpus (2)

• Periods of the multiple Berglund-Huebsch-Krawitz mirrors
• On Calabi-Yau manifolds in weighted projective spaces and their mirror GLSMs