On the Intersection Points of Two Plane Algebraic Curves

被引：1

作者：

Hakopian, H. ^{[1
]}

Voskanyan, D. ^{[1
]}

机构：

[1] Yerevan State Univ, Yerevan, Armenia

来源：

JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES | 2019年 / 54卷 / 02期

关键词：

Plane curve; intersection point; bivariate interpolation; fundamental polynomial; n-poised set; n-independent set;

D O I：

10.3103/S1068362319020055

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a set X, #X = mn, m n, is the set of intersection points of some two plane algebraic curves of degrees m and n, respectively, if and only if the following conditions are satisfied: a) Any curve of degree m+ n - 3 containing all but one point of X, contains all of X, b) No curve of degree less than m contains all of X.The conditions a) and b) in theonly if direction of this result follow fromthe Ceyley-Bacharach and Noether theorems, respectively.

引用

页码：90 / 97

页数：8

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