Ebeling, W.; Gusein-Zade, S. M. Monodromy of dual invertible polynomials. (English) Zbl 1257.32028 Mosc. Math. J. 11, No. 3, 463-472 (2011). Summary: A generalization of Arnold’s strange duality to invertible polynomials in three variables by the first author and A. Takahashi [Compos. Math. 147, No. 5, 1413–1433 (2011; Zbl 1238.14029)] 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 \(f^{T}\). 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 \(f^{T}\). Cited in 1 ReviewCited in 2 Documents MSC: 32S05 Local complex singularities 32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects) 14J33 Mirror symmetry (algebro-geometric aspects) Keywords:invertible polynomials; monodromy zeta functions; Saito duality Citations:Zbl 1238.14029 PDFBibTeX XMLCite \textit{W. Ebeling} and \textit{S. M. Gusein-Zade}, Mosc. Math. J. 11, No. 3, 463--472 (2011; Zbl 1257.32028) Full Text: arXiv Link