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Equisingular Families of Projective Curves

  • Chapter
Global Aspects of Complex Geometry

Summary

In this survey, we report on progress concerning families of projective curves with fixed number and fixed (topological or analytic) types of singularities. We are, in particular, interested in numerical, universal and asymptotically proper sufficient conditions to guarantee the nonemptyness, T-smoothness and irreducibility of the variety of all projective curves with prescribed singularities in a fixed linear system. We also discuss the analogous problem for hypersurfaces of arbitrary dimension with isolated singularities, and we close with a section on open problems and conjectures.

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Authors and Affiliations

  1. Fachbereich Mathematik, TU Kaiserslautern, Erwin-Schrödinger-Straße, 67663, Kaiserslautern, Germany

    Gert-Martin Greuel, Christoph Lossen & Eugenii Shustin

  2. School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Gert-Martin Greuel, Christoph Lossen & Eugenii Shustin

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  1. Gert-Martin Greuel
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  2. Christoph Lossen
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  1. Lehrstuhl Mathematik VIII, Mathematisches Institut, Universität Bayreuth, 95440, Bayreuth, Germany

    Fabrizio Catanese

  2. Mathematik, Universität Duisburg-Essen, 45117, Essen, Germany

    Hélène Esnault

  3. Institut für Mathematik, Universität Bochum, Universitätsstraße 150, 44801, Bochum, Germany

    Alan T. Huckleberry

  4. FB Mathematik, Institut für Mathematik, Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    Klaus Hulek

  5. Lehrstuhl Mathematik I, Mathematisches Institut, Universität Bayreuth, 95440, Bayreuth, Germany

    Thomas Peternell

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Greuel, GM., Lossen, C., Shustin, E. (2006). Equisingular Families of Projective Curves. In: Catanese, F., Esnault, H., Huckleberry, A.T., Hulek, K., Peternell, T. (eds) Global Aspects of Complex Geometry. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-35480-8_5

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