论文标题
结果，有关代数曲线通过$ n $独立的节点
On a result concerning algebraic curves passing through $n$-independent nodes
论文作者
论文摘要
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 $通过$ \ Mathcal X的所有节点。$我们提供了恰好有三个此类曲线的情况的表征。也就是说，我们证明当时的$ \ Mathcal X $具有特殊的结构：其所有节点都属于$ n-2 $ n-2，$或所有节点的曲线，但三个节点均属于$ n-3的（最大）曲线。$ n-3。 该结果补充了H. Kloyan，D。Voskanyan和H. H.最近确定的结果，请注意，这两个结果的证明是完全不同的。
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 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. H. Note that the proofs of the two results are completely different.
