Double point curves for corank \(2\) map germs from \(\mathbb{C}^2\) to \(\mathbb{C}^3\)
This is a well-written paper which gives an instructive description of properties of finitely determined map germs \(f:(\mathbb C^{2},0) \to (\mathbb C^{3},0).\) The authors extend to corank 2 map-germs properties and formulae proved in [\textit{W. L. Marar} and \textit{D. Mond}, J. Lond. Math. Soc., II. Ser. 39, No. 3, 553--567 (1989; Zbl 0691.58015)] for corank 1 finitely determined germs. They also give an explicit description of the double point scheme in terms of elementary symmetric functions and provide explicit calculations in the corank 2 case. The final section of the paper is dedicated to the proof of the following result: the Whitney equisingularity of \(1\)-parameter families of map germs \(f_t:(\mathbb C^{2},0) \to (\mathbb C^{3},0)\) is equivalent to the constancy both of \(\mu(D(f_t))\) and \(\mu(f_t(\mathbb C^2) \cap H)\) with respect to \(t,\) where \(H \subset \mathbb C^3\) is a generic hyperplane.
scientific article; zbMATH DE number 6011305
scientific article