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Determinacy of smooth germs with real isolated line singularities. (English) Zbl 0971.58024
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 \(\Sigma(f)\) [D. Siersma, Proc. Symp. Pure Math. 40, Part 2, 485-496 (1983; Zbl 0514.32007)].
In this paper the analogue for real analytic or smooth functions is proved.

MSC:
58K40 Classification; finite determinacy of map germs
32S05 Local complex singularities
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