We describe a relation between Arnold’s strange duality and a polar duality between the Newton polytopes which is mostly due to M. Kobayashi. We show that this relation continues to hold for the extension of Arnold’s strange duality found by C. T. C. Wall and the author. By a method of Ehlers-Varchenko, the characteristic polynomial of the monodromy of a hypersurface singularity can be computed...

M. Kobayashi introduced a notion of duality of weight systems. We tone this notion slightly down to a notion called coupling. We show that coupling induces a relation between the reduced zeta functions of the monodromy operators of the corresponding singularities generalizing an observation of K. Saito concerning Arnold's strange duality. We show that the weight systems of the mirror symmetric ...

We will show that the duality for regular weight system introduced by K. Saito can be interpreted as the duality for the orbifoldized Poincare polynomial χ(W,G)(y, ȳ). Introduction In [A], Arnold discovered a strange duality among the 14 exceptional singularities. This was interpreted by Dolgachev, Nikulin and Pinkham in terms of the duality between algebraic cycles and transcendental cycles on...

In [E6] a relation is proved between the Poincaré series of the coordinate algebra of a two-dimensional quasihomogeneous isolated hypersurface singularity and the characteristic polynomial of its monodromy operator. We study this relation for Fuchsian singularities and show that it is connected with the mirror symmetry of K3 surfaces and with automorphisms of the Leech lattice. We also indicate...

We prove the strange duality for parabolic symplectic bundles on a pointed projective line.