Milnor fibre homology via deformation for non-isolated singularities

We study hypersurfaces of dimension n with a 1-dimensional singular set and consider admissible deformations for the study of the Milnor fibre. It’s homology depends very much on the types of special singularities in the deformation. In dimension n-1  there are strong bounds related to the minimum of the  n-1 Betti numbers of the transversal MIinor  fibres. In several cases we can even show that the homology is concentrated in dimension n only.  The same technique has been used by us to compute the vanishing homology of projective hypersurfaces with a 1-dimensional singular set. This is joint work with Mihai Tibar.