Proof of the Main Algorithm

Abstract

The algorithm and its proof is a highly generalized version of the algorithm which determines the resolution graph of cyclic coverings. Its origin goes back to the case of suspensions, when one starts with an isolated plane curve singularity $f^{\prime}$ and a positive integer n, and one determines the resolution graph of the hypersurface singularity$\{f^{\prime}(x,y)+z^n=0\}$ from the embedded resolution graph of $f^{\prime}$ and the integer n; see 5.3.