Equisingular Families of Projective Curves

Details Equisingular Families of Projective Curves Equisingular Families of Projective Curves

2006-12-12

arxiv.org/abs/math/0612310v1

Global Aspects of Complex Geometry, Springer Verlag (2006), 171-210

Mathematics

Algebraic Geometry

39 pages

Scientific paper

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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