Some classes of line singularities
type: Item
instance of: scholarly article
title: Some classes of line singularities
zbMATH Open document ID: 0628.32028
DOI: 10.1007/BF01162870
author: Theo de Jong
published in: Mathematische Zeitschrift
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173940
review text: 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.
Mathematics Subject Classification ID: 32G05
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 32Sxx
Mathematics Subject Classification ID: 32S30
zbMATH DE Number: 4021591
zbMATH Keywords: germs of holomorphic functions
zbMATH Keywords: isolated line singularities
zbMATH Keywords: deformation
MaRDI profile type: Publication
cites work: Singular Points of Complex Hypersurfaces. (AM-61)
cites work: Q3717380
cites work: Q3660073
cites work: Singularities with critical locus a 1-dimensional complete intersection and transversal type \(A_ 1\)
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description: scientific article; zbMATH DE number 4021591