ИСТИНА

Arnold’s strange duality between exceptional unimodal hypersurface singularities seems to be the first observation of a mirror symmetry effect. Initially this duality was formulated in terms of Gabrielov and Dolgachev numbers of the singularities. The characteristic polynomials of the monodromy operators of dual singularities are related by the Saito duality. A generalization of the Arnold duality is the Berglund-Hübsch-Henningson duality between the so-called invertible polynomials. In their works these polynomials appeared as superpotentials in mirror-symmetric Landau-Ginzburg models. In the orbifold (Berglund–Henningson) setting this duality treats a pair consisting of an invertible polynomial and a (finite abelian) group of its symmetries together with a dual pair. We shall describe some dualities related with the actions of the symmetry groups on the corresponding Milnor fibres. They include coincidence of certain orbifold type invariants and an equivariant version of the Saito duality. The talk is based on joint works with W.Ebeling.