ON THE MINIMAL NUMBER OF NODES UNIQUELY DETERMINING ALGEBRAIC CURVES

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Submitted: 2025-02-11; Published: 2025-02-11

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Abstract

It is well-known that exactlyN−1n-independent nodes uniquely determinethe curve of degreenpassing through them, whereN=12(n+1)(n+2).It wasproved in [1], that at leastN−4 number ofn-independent nodes are neededto determine the curve of degreen−1 uniquely. The paper has also posed aconjecture concerning the analogous problem for general degreek≤n.In thepresent paper the conjecture is proved, establishing that the minimal number ofn-independent nodes uniquely determining the curve of degreek≤nis equalto(k−1)(2n+4−k)2+2.