Perverse Results on Milnor Fibers Inside Parameterized Hypersurfaces

We present results on the cohomology of Milnor fibers inside parameterized hypersurfaces that follow directly from techniques in the category of perverse sheaves. In particular, we define a new perverse sheaf, the multiple-point complex of the parameterization, which naturally arises when studying how the multiple-point set influences the topology of the Milnor fiber. Applications to stable unfoldings of finite maps with isolated instabilities are also discussed.

Publications of the Research Institute for Mathematical Sciences, Vol. 52, Pages 413–433