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Equisingular Families of Projective Curves

In: Global Aspects of Complex Geometry

Author

Listed:
  • Gert-Martin Greuel

    (TU Kaiserslautern, Fachbereich Mathematik
    Tel Aviv University, School of Mathematical Sciences)

  • Christoph Lossen

    (TU Kaiserslautern, Fachbereich Mathematik
    Tel Aviv University, School of Mathematical Sciences)

  • Eugenii Shustin

    (TU Kaiserslautern, Fachbereich Mathematik
    Tel Aviv University, School of Mathematical Sciences)

Abstract

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.

Suggested Citation

  • Gert-Martin Greuel & Christoph Lossen & Eugenii Shustin, 2006. "Equisingular Families of Projective Curves," Springer Books, in: Fabrizio Catanese & Hélène Esnault & Alan T. Huckleberry & Klaus Hulek & Thomas Peternell (ed.), Global Aspects of Complex Geometry, pages 171-209, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-35480-2_5
    DOI: 10.1007/3-540-35480-8_5
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