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The Geometry of Families of Singular Curves

  • Chapter
New Developments in Singularity Theory

Part of the book series: NATO Science Series ((NAII,volume 21))

Abstract

It is a classical and interesting problem, which is still in the centre of theoretical research, to study the variety V of (reduced, irreducible) curves C ⊂ ℙ 2 = ℙ 2(ℂ) of degree d having exactly r singularities of prescribed (topological or analytic) types S 1,…, S r . Among the most important questions are:

  • Is V ≠ θ (existence problem)?

  • Is V irreducible (irreducibility problem)?

  • Is V smooth and of expected dimension (T-smoothness problem)?

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Universität Kaiserslautern, Germany

    Gert-Martin Greuel & Christoph Lossen

Authors
  1. Gert-Martin Greuel
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  2. Christoph Lossen
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University Utrecht, Utrecht, The Netherlands

    D. Siersma

  2. Mathematical Sciences, Liverpool, UK

    C. T. C. Wall

  3. Moscow Aviation Institute, Moscow, Russian Republic

    V. Zakalyukin

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Greuel, GM., Lossen, C. (2001). The Geometry of Families of Singular Curves. In: Siersma, D., Wall, C.T.C., Zakalyukin, V. (eds) New Developments in Singularity Theory. NATO Science Series, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0834-1_7

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  • DOI: https://doi.org/10.1007/978-94-010-0834-1_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6997-4

  • Online ISBN: 978-94-010-0834-1

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