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Equianalytic and equisingular families of curves on surfaces

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Summary

We consider flat families of reduced curves on a smooth surfaceS such that each memberC has the same number of singularities and each singularity has a fixed singularity type (up to analytic resp. topological equivalence). We show that these families are represented by a schemeH and give sufficient conditions for the smoothness ofH (atC). Our results improve previously known criteria for families with fixed analytic singularity type and seem to be quite sharp for curves in ℙ2 of small degree. Moreover, for families with fixed topological type this paper seems to be the first in which arbitrary singularities are treated.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Kaiserslautern, Erwin-Schrödinger-Straße, D-67663, Kaiserslautern

    Gert-Martin Greuel & Christoph Lossen

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  1. Gert-Martin Greuel
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  2. Christoph Lossen
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Greuel, GM., Lossen, C. Equianalytic and equisingular families of curves on surfaces. Manuscripta Math 91, 323–342 (1996). https://doi.org/10.1007/BF02567958

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  • DOI: https://doi.org/10.1007/BF02567958

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