Interpolation for Normal Bundles of General Curves

Given $n$ general points $p_1, p_2, \ldots, p_n \in \mathbb P^r$, it is natural to ask when there exists a curve $C \subset \mathbb P^r$, of degree $d$ and genus $g$, passing through $p_1, p_2, \ldots, p_n$. In this paper, the authors give a complete answer to this question for curves $C$ with nonspecial hyperplane section.