Perverse Results on Milnor Fibers inside Parameterized Hypersurfaces

Abstract

We discuss some results for the cohomology of Milnor fibers inside parameterized hypersurfaces which follow quickly from results in the category of perverse sheaves. In particular, we define a new perverse sheaf called the multiple-point complex of the parameterization, which naturally arises when investigating how the multiple-point set influences the topology of the Milnor fiber. We also discuss applications to stable unfoldings of finite maps with isolated instabilities.