Counting singularities via Fitting ideals (Q2888828)

The authors consider a finitely determined map germ \(f: (\mathbb C^{n+m}, 0)\to (\mathbb C^{m}, 0)\) with only singularities of type \(A_k\), and give a formula for the number of isolated singularities. They apply the result of \textit{D. Mond} and \textit{R. Pellikaan} [Lect. Notes Math. 1414, 107--161 (1989; Zbl 0715.32007)] and express the number of the singularities by means of the dimension of the Artinian algebra associated to certain fitting ideals. For the case \(m = 3\), the authors provide a way to compute the number of ordinary triple points. Furthermore if \(f\) is of co-rank one, they compute the number of points formed by the intersection between a germ of a cuspidal edge and a germ of a plane. In the last section, several examples, including cases with co-rank two or \(m=n=4\) are shown.