2015; Physical and Mathematical Sciences, 49(3 (238): 17–22
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ON THE MINIMAL NUMBER OF NODES UNIQUELY DETERMINING ALGEBRAIC CURVES

Sofi Toroyan*

Received: 2025-02-11 · Published: 2015-12-15

© 2015 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
ON THE MINIMAL NUMBER OF NODES UNIQUELY DETERMINING ALGEBRAIC CURVES
Author
Sofi Toroyan
Published
2015-12-15
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.46991/PYSUA.2015.49.3.017

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.
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