A. Hirschowitz et al., SOME BRILL-NOETHER STRATA OF THE HILBERT SCHEME OF P2, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 319(6), 1994, pp. 589-594
We determine for N > d (d + 3)/2 the irreducible components of the sch
eme of subschemes of degree N of P2 contained in a pencil of curves of
degree d.