Curves and their hyperplane sections

Let C be curve in Pkn over an algebraically closed field k of characteristic 0 and let Γ=C∩H be the generic hyperplane section. It is known that, if C is reduced and irreducible, then Γ consists of points in uniform position. Assume instead that Γ is not in uniform position; then Γ contains a subscheme Γ′ of degree d′ such that hΓ′(s)