Zariski’s dimensionality type of singularities. Case of dimensionality type 2

In the 1970s O. Zariski introduced a general theory of equisingularity for algebroid and algebraic hypersurfaces over an algebraically closed field characteristic zero. His builds up on understanding dimensionality type hypersurface singularities, notion defined recursively by considering discriminants loci successive “generic” corank 1 1 projections. The singularities 1, that is ones appearing generically in codimension was developed his foundational papers equisingular families plane curve singularities. this paper we completely settle case 2, studying surfaces not necessarily isolated, three-dimensional space.