On the uniqueness of algebraic curves

It is well-known that $N-1$ $n$-independent nodes uniquely determine curve of degree $n,$ where $N=(1/2)(n+1)(n+2).$ We are interested in finding the minimal number of $n$-independent nodes determining uniquely curve of degree $k\le n-1.$ In this paper we show that this number for $k=n-1$ is $N-4$.