Singularities with critical locus a 1-dimensional complete intersection and transversal type A1

AbstractIn this paper we study germs of holomorphic functions f: (Cn+1,0)→C with the following two properties: (i)the critical set Σ of f is a 1-dimensional isolated complete intersection singularity (icis);(ii)the transversal singularity of f in points of Σ−{0} is of type A1. We first compute the homology of the Milnor fibre F of f in terms of numbers of special points in certain deformations. Next we show that the homotopy type of the Milnor fibre F of f is a bouquet of spheres. There are two cases: (a)general case Sn v⋯v Sn(b)special case Sn-1 v sn v⋯v Sn