Singularities of dimensionality type 1

We study the equisingularity of singularities of dimensionality type 1 (following Zariski’s terminology) for varieties that are not necessarily hypersurfaces. We view each variety as a family of space curves, some of them being nonreduced, and we characterize the simultaneous resolution of the family by means of some invariants of the curves of the family. The results can be applied for the study of the equisingularity theory supported on the stratification by simultaneous resolvability of singularities.