论文标题
复杂平面中并发线的Sylvester-Gallai结果
A Sylvester-Gallai result for concurrent lines in the complex plane
论文作者
论文摘要
我们表明，如果$ \ mathbb {c}^2 $中的一组点位于$ m $并发线的家族上，并且其中一条线包含超过$ m-2 $点，则有一条线经过该集合的两个点。我们的结果中绑定的$ M-2 $是最佳的。我们的主要定理解决了Frank de Zeeuw的猜想，并概括了Kelly和Nwankpa的结果。
We show that if a set of points in $\mathbb{C}^2$ lies on a family of $m$ concurrent lines, and if one of those lines contains more than $m-2$ points, then there is a line passing through exactly two points of the set. The bound $m-2$ in our result is optimal. Our main theorem resolves a conjecture of Frank de Zeeuw, and generalizes a result of Kelly and Nwankpa.
