The topological types of hypersurface simple K 3 singularities

Abstract

We give a result that relates the diffeomorphism type of the link of a nondegenerate semi-quasi-homogeneous hypersurface simple K3 singularity with the singularities of the normal K3 surface that appears as the exceptional divisor of the resolution of the singularity. As a result, we show that the links are diffeomorphic to the connected sum of copies of S 2 × S 3 . Moreover, we also show that the topological types of hypersurface simple K3 singularities defined by non-degenerate semi-quasihomogeneous polynomials are all different.