The Poincaré series of some special quasihomogeneous surface singularities

Abstract

In the author's paper ''Poincaré series and monodromy of a two-dimensional quasihomogeneous hypersurface singularity'' 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 relations between other singularities and Conway's group.