Monodromy of Dual Invertible Polynomials

A generalization of Arnold’s strange duality to invertible polynomials in three variables by the first author and A. Takahashi includes the following relation. For some invertible polynomials f the Saito dual of the reduced monodromy zeta function of f coincides with a formal “root” of the reduced monodromy zeta function of its Berglund– Hübsch transpose f . Here we give a geometric interpretation of “roots” of the monodromy zeta function and generalize the above relation to all non-degenerate invertible polynomials in three variables and to some polynomials in an arbitrary number of variables in a form including “roots” of the monodromy zeta functions both of f and f . 2000 Math. Subj. Class. 32S05, 32S40, 14J33.