Equisingular families of projective curves

Gert Martin Greuel, Christoph Lossen, Eugenii Shustin

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

6 Scopus citations


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.

Original languageEnglish
Title of host publicationGlobal Aspects of Complex Geometry
PublisherSpringer Berlin Heidelberg
Number of pages39
ISBN (Print)3540354794, 9783540354796
StatePublished - 2006


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