Equianalytic and equisingular families of curves on surfaces

Details Equianalytic and equisingular families of curves on surfaces Equianalytic and equisingular families of curves on surfaces

1995-03-21

arxiv.org/abs/alg-geom/9503011v1

Mathematics

Algebraic Geometry

LaTeX v 2.09

Scientific paper

We consider flat families of reduced curves on a smooth surface S such that each member C has the same number of singularities of fixed singularity types and the corresponding (locally closed) subscheme H of the Hilbert scheme of S. We are mainly concerned with analytic resp. topological singularity types and give a sufficient condition for the smoothness of H (at C). Our results for S=P^2 seem to be quite sharp for families of cuves of small degree d.

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