ON THE MINIMAL NUMBER OF NODES UNIQUELY DETERMINING ALGEBRAIC CURVES

Abstract

It is well-known that exactly $N-1$ n-independent nodes uniquely determine the curve of degree n passing through them, where $N=\dfrac{1}{2}(n+1)(n+2).$ It was proved in [1], that at least $N-4$ number of n-independent nodes are needed to determine the curve of degree $n-1$ uniquely. The paper has also posed a conjecture concerning the analogous problem for general degree $k\le n$. In the present paper the conjecture is proved, establishing that the minimal number of n-independent nodes uniquely determining the curve of degree $k\le n$ is equal to $\dfrac{(k-1)(2n+4-k)}{2}+2.$