SINGULARITIES IN CODIMENSION 1 OF THE HILBERT SCHEME. AN EXAMPLE.

Jan O. Kleppe

In the Hilbert scheme H(d,g) of smooth space curves of degree d and genus g we give an example of a reduced irreducible component V which is not normal. More precisely there is a reduced component V of H(16,29) whose general curve is Buchsbaum with 1-dimensional Rao module, containing a proper closed Z such that H(16,29) and V is singular along Z.