Residual equisingularity

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