Zariski’s Conjecture

Abstract: We give a historical presentation of Zariski’s Conjecture and its local version. The ‘original’ (global) version is the following: the multiplicity of an isolated complex analytic hypersurface singularity is determined by its embedded topological type. The local version is the following: along a Milnor-number constant flat deformation of isolated hypersurface singularities the multiplicity is constant.