A remark on vanishing cycles with two strata
arXiv:1108.3945
Abstract
Suppose that the critical locus of a complex analytic function on affine space is, itself, a space with an isolated singular point at the origin $\0$, and that the Milnor number of restricted to normal slices of $Σ-\{\0\}$ is constant. Then, the general theory of perverse sheaves puts severe restrictions on the cohomology of the Milnor fiber of at $\0$, and even more surprising restrictions on the cohomology of the Milnor fiber of generic hyperplane slices.
A 3-page note