Lê's conjecture on equisingular deformations of plane curve singularities

Let $(V(f),\0) \subseteq ({\mathbb C}^3,\0)$ be a reduced hypersurface with $\dim_\0 \Sigma f=1$, and suppose that the normalization of $V(f)$ is a bijection. Lê's conjecture. Then $V(f)$ is the total space of an equisingular deformation of plane curve singularities. This conjecture concerns the geometric significance of simultaneous normalization for parameterized surfaces and its relation to equisingularity; the source poses it in connection with the perverse sheaf $\operatorname{Gr}_0^W {\mathbb Q}_{V(f)}^\bullet[2]$.