Counting isolated singularities in germs of applications ${\C^n,0\to \C^p,0}$, n<p

Abstract

In this paper we give a formula for counting the number of isolated stable singularities of a stable perturbation of corank 1 germs $f:\C^n,0\to \C^p,0$ with $n<p$ that appear in the image $f(\C^n).$ We also define a set of ${\cal A}$-invariants and show that their finiteness is a necessary and sufficient condition for the ${\cal A}$-finiteness of the germ $f.$