Strange duality between hypersurface and complete intersection singularities (Q338642)

In [Russ. Math. Surv. 30, No. 5, 1--75 (1975; Zbl 0343.58001)], \textit{V. I. Arnol'd} discovered a strange duality between the 14 exceptional unimodal singularities. Somewhat later an extension of Arnold's duality was described for bimodal hypersurface singularities and isolated complete intersections of dimension two in \(\mathbb C^4\) (see [\textit{W. Ebeling} and \textit{C. T. C. Wall}, Compos. Math. 56, 3--77 (1985; Zbl 0586.14033)]). The paper under review aims to derive this duality using the mirror symmetry and the operation of transposition of invertible polynomials defined in [\textit{P. Berglund} and \textit{T. Hübsch}, Nucl. Phys., B 393, No. 1--2, 377--391 (1993; Zbl 1245.14039)]. Among other things, the authors explain some features of their construction in terms of Dolgachev and Gabrielov numbers, Coxeter-Dynkin diagrams for distinguished bases of vanishing cycles, Milnor lattices, and so on.