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).