Prepolar deformations and a new Lê-Iomdine formula (Q2365029)

We describe a class of deformations of affine hypersurface singularities. These deformations, which we call prepolar deformations, are the ones which we found to be important in our work on the Lê numbers of a hypersurface singularity. However, the results of this paper are not directly related to our work on the Lê numbers. The main result of this paper is to use prepolar deformations to put lower bounds on the top Betti number of the Milnor fibre of a non-isolated hypersurface singularity. These lower bounds are a corollary of a generalization of the formula of Lê and Iomdine.