Minimal Whitney stratification and Euler obstruction of discriminants
The authors show how to obtain the minimal Whitney stratification of the discriminant of finitely determined map germs from \((\mathbb{C}^m,0)\) to \((\mathbb{C}^p,0)\), of corank one if \(n<p\), and only with \(A_k\) singularities, when \(m=n+p\) with \(n\geq 0\). They prove that for the pairs above, this stratification coincides with the stratification in the general theory developed by T. Gaffney for discriminants of any finitely determined holomorphic map germ in the nice dimensions of J. Mather (Theorem 3 and Theorem 6). The local Euler obstruction at \(0\), in a class of discriminants of finitely determined map germs from \((\mathbb{C}^{n+p},0)\) to \((\mathbb{C}^p,0)\) with \(n\geq 0\) and only with \(A_k\) singularities, is also computed.
scientific article; zbMATH DE number 6686314
scientific article