Determinacy of smooth germs with real isolated line singularities (Q2716125)

Let \((V(f),0) \subseteq (\mathbb{C}^n,0)\) be the germ of an isolated line singularity (i.e., a non-isolated singularity such that the singular locus \(\Sigma(f)\) is a smooth curve and the transversal sections are \(A_1\) singularities). Those singularities are finitely determined inside the space of singularities with singular locus containing \(\Sigma(f)\) [\textit{D. Siersma}, Proc. Symp. Pure Math. 40, Part 2, 485-496 (1983; Zbl 0514.32007)]. NEWLINENEWLINENEWLINEIn this paper the analogue for real analytic or smooth functions is proved.