On the minimal number of nodes uniquely determining algebraic curves (Հանրահաշվական կորերը միակորեն որոշող հանգույցների փոքրագույն քանակի վերաբերյալ )

Abstract

It is well-known that the number of n-independent nodes determining uniquely the curve of degree n passing through them equals to N − 1, where N = 1 2 (n + 1)(n + 2). It was proved in [1], that the minimal number of n-independent nodes determining uniquely the curve of degree n − 1 equals to N −4. The paper also posed a conjecture concerning the analogous problem for general degree k ≤ n. In the present paper the conjecture is proved, establishing that the minimal number of n-independent nodes determining uniquely the curve of degree k ≤ n equals to (k −1)(2n+4−k) 2 +2.