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Défaut de postulation et singularités du schéma de Hilbert. (French) Zbl 0577.14019
The main result of this paper is a quite general procedure for constructing smooth connected curves in projective 3-space which are singular points on the Hilbert scheme, sitting on a reduced component. One starts by constructing a flat family of curves where the special fiber is contained in a surface of smaller degree than expected. Using liaison, this jumping behaviour is inherited by the cohomology of the normal bundles of the linked curves.
It is still open whether there exists such an example which lies in only one irreducible component of the Hilbert scheme.
Reviewer: S.A.Strømme

14H10 Families, moduli of curves (algebraic)
14H20 Singularities of curves, local rings
14C05 Parametrization (Chow and Hilbert schemes)
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)