Let V V be a complex analytic set and Sg ⁡ V \operatorname {Sg} V the singular set of V V be in codimension one; then the set of points of Sg ⁡ V \operatorname {Sg} V for which V V is not residually equisingular along Sg ⁡ V \operatorname {Sg} V is a proper analytic subset of Sg ⁡ V \operatorname {Sg} V . V V is said to be residually equisingular along Sg ⁡ V \operatorname {Sg} V if all one dimensional slices of V V transverse to Sg ⁡ V \operatorname {Sg} V have isomorphic resolutions.