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Deformationen isolierter Kurvensingularitäten mit eingebetteten Komponenten

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Abstract

We study deformations of isolated curve singularities of arbitrary embedding dimension which may have embedded components. The existence of an embedded component has the effect that the generic fibre consists of isolated (fat) points and disjoint 1-dimensional components. We introduce for isolated curve singularities and for fat points a Milnor number μ and a σ-invariant which generalize the well known invariants for reduced curve singularities. The invariants μ, σ and the length of the embedded component control the topology of the generic fibre in a way which is surprisingly similar to the case of reduced curves, although many new phenomena occur.

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Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Fernuniversität Hagen, 5800, Hagen

    Christian Brücker

  2. Fachbereich Mathematik, Universität Kaiserslautern, 6750, Kaiserslautern

    Gert-Martin Greuel

Authors
  1. Christian Brücker
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  2. Gert-Martin Greuel
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This article was processed by the author using the Springer-Verlag TEX mamath macro package 1990.

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Brücker, C., Greuel, GM. Deformationen isolierter Kurvensingularitäten mit eingebetteten Komponenten. Manuscripta Math 70, 93–114 (1991). https://doi.org/10.1007/BF02568363

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  • DOI: https://doi.org/10.1007/BF02568363

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