Some classes of line singularities
We study some classes of germs of holomorphic functions with a smooth one-dimensional critical locus. One such class,the so-called isolated line singularities, has been studied by \textit{D. Siersma} [Proc. Symp. Pure Math. 40, Part 2, 485-496 (1983; Zbl 0514.32007)]. For each germ f in a class, we prove that there exists a deformation g of f, such that g has only special types of singularities which can be given explicitely. Furthermore, for each special type, the number of them occuring in the deformation g, can be given by algebraic formulas in terms of f. This has been done in the isolated line singularity case by \textit{R. Pellikaan} [Hypersurface singularities and resolutions of Jacobi modules, Thesis, Rijksuniv. Utrecht (1985)] and \textit{D. Siersma} [loc. cit.]. The number of special types of singularities in the deformation g are closely related to the homotopy type of the Milnor fibre of f.
scientific article; zbMATH DE number 4021591
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