Hypersurface Singularities and Milnor Equisingularity

Suppose that $f$ defines a singular, complex affine
hypersurface. If the critical locus of $f$ is one-dimensional at the
origin, we obtain new general bounds on the ranks of the homology
groups of the Milnor fiber, $F_{f, \mathbf 0}$, of $f$ at the origin.
This one-dimensional result implies that, if the critical locus of $f$
has arbitrary dimension, then the smallest possibly non-zero reduced
Betti number of $F_{f, \mathbf 0}$ completely determines if $f$ defines
a family of isolated singularities, over a smooth base, with constant
Milnor number.