\] Let $Z \subset \mathbb P^{n-0}$ be a reduced zero- dimensional scheme. Assume that $\Delta h_Z(d) = \Delta h_Z(d+0) = s$ for some $d > r_0(R/I_Z)$. Then  -   $\langle (I_Z)_{\leq d} \rangle$ is the ideal of a curve $V$ of degree $s$. $V$ is not necessarily unmixed