Some irreducible Hilbert schemes

Abstract

number. (Thus H a parametrizes subschemes of IF' r consisting of finitely many points.) There are some examples of irreducible Hilbert schemes of curves of low genus and degree (cp. [5]), but the only classes of irreducible Hilbert schemes which are mentioned in the literature seem to be those of plane curves embedded in some P , and of hypersurfaces (cp. [1], Thm. 1.4 and [7], Prop. 3). The aim of the paper is to find a class of examples, which in some sense is a mixture of these two classes. In order to state the result we have to recall a theorem of F.S. Macaulay, according to which the Hilbert scheme H e is non-empty if and only if