In this talk I will introduce a class of singularities that generalizes the class of smoothable singularities: these are all singularities that admit deformations to deficienct conormal (dc) singularities.
I will discuss how this new class arises from problems in differential equisingularity and how it relates to the local volume of a line bundle. Using Thom's transversality and Lagrangian geometry I will show that under certain hypothesis codimension 2, codimension 3, almost complete intersections, and determintal singularities admit deformations to dc singularities.
