Orbifold E-functions of dual invertible polynomials

Abstract

An invertible polynomial is a quasihomogeneous polynomial with the number of monomials coinciding with the number of variables and such that the weights of the variables and the quasi-degree are well defined. In the framework of the search for mirror symmetric orbifold Landau-Ginzburg models, P.~Berglund and M.~Henningson considered a pair $(f,G)$ consisting of an invertible polynomial $f$ and an abelian group $G$ of its symmetries together with a dual pair $(\tilde{f},\tilde{G})$. We consider the so-called orbifold E-function of such a pair $(f,G)$ which is a generating function for the exponents of the monodromy action on an orbifold version of the mixed Hodge structure on the Milnor fibre of $f$. We prove that the orbifold E-functions of Berglund-Henningson dual pairs coincide up to a sign depending on the number of variables. The proof is based on a relation between monomials (say, elements of a monomial basis of the Milnor algebra of an invertible polynomial) and elements of the whole symmetry group of the dual polynomial.

12 pages

References in corpus (1)

• FJRW rings and Landau-Ginzburg Mirror Symmetry

Cited by in corpus (5)

• Orbifold Jacobian algebras for invertible polynomials
• Maximally-graded matrix factorizations for an invertible polynomial of chain type
• On the stringy Hodge numbers of mirrors of quasi-smooth Calabi-Yau hypersurfaces
• Gamma integral structure for an invertible polynomial of chain type
• Lattices for Landau-Ginzburg orbifolds