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 Sigma(i) has codimension n in the correspo nding jet space J(k)(n, p). When its iterated successors have codimension l arger than n, the paper gives a list of situations in which the number of S igma(i) points that appear in a generic deformation of f can be computed al gebraically by means of Jacobian ideals of f. This list can be summarised i n the following way: f must have rank n - i(1) and, in addition, in the cas e p = 6, f must be a singularity of type Sigma(i2.i2).