On the Number of Singularities in Generic Deformations of Map Germs

Let f :C n , 0→C p , 0 be a K‐finite map germ, and let i =( i 1 , …, i k ) be a Boardman symbol such that ∑ i has codimension n in the corresponding jet space J k ( n , p ). When its iterated successors have codimension larger than n , the paper gives a list of situations in which the number of ∑ i points that appear in a generic deformation of f can be computed algebraically by means of Jacobian ideals of f . This list can be summarised in the following way: f must have rank n − i 1 and, in addition, in the case p =6, f must be a singularity of type∑ i 1 , i 2.