Singular Milnor fibers and higher multiplicities (Q1356254)

A class of non-isolated singularities is studied, which still have some nice properties as isolated hypersurface singularities, the class of almost free divisors. This class contains discriminants of finitely determined map germs, bifurcation sets of certain unfoldings of hypersurfaces, certain central arrangements of hyperplanes. To these singularities a so-called singular Milnor fibration is associated, which has similar properties as the Milnor fibration for isolated singularities. Especially, there is a ``singular'' Milnor number and higher multiplicities similar to Teissier's \(\mu^*\). They are used to deduce topological properties of these singularities.