On the Spectrum of Curve Singularities

There is the following crucial problem in the singularity theory: how can we recognize that a singular germ is hypersurface, or complete intersection singularity. Or: is there any criterion which distinguishes the isolated hypersurface singularities among the isolated singularities? These kind of questions arise in many areas of the algebraic geometry and singularity theory, we mention here only one. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.