Geodesic
On a result concerning algebraic curves passing through $n$-independent nodes
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 56 (2022) no. 3, pp. 97-106

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Let a set of nodes $\mathcal X$ in the plane be $n$-independent, i.e. each node has a fundamental polynomial of degree $n.$ Assume that $\#\mathcal X=d(n,n-3)+3= (n+1)+n+\cdots+5+3.$ In this paper we prove that there are at most three linearly independent curves of degree less than or equal to $n-1$ that pass through all the nodes of $\mathcal X.$ We provide a characterization of the case when there are exactly three such curves. Namely, we prove that then the set $\mathcal X$ has a very special construction: either all its nodes belong to a curve of degree $n-2,$ or all its nodes but three belong to a (maximal) curve of degree $n-3.$ This result complements a result established recently by H. Kloyan, D. Voskanyan, and H. Hakopian. Note that the proofs of the two results are completely different.
Keywords: algebraic curve, fundamental polynomial, $n$-independent nodes.
Mots-clés : maximal curve 
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     title = {On  a  result  concerning algebraic  curves  passing  through $n$-independent nodes},
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     pages = {97--106},
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     language = {en},
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H. A. Hakopian. On  a  result  concerning algebraic  curves  passing  through $n$-independent nodes. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 56 (2022) no. 3, pp. 97-106. http://geodesic.mathdoc.fr/item/UZERU_2022_56_3_a1/