论文标题
Cubic曲线的Sylvester-Gallai定理
A Sylvester-Gallai theorem for cubic curves
论文作者
论文摘要
我们证明了Cubics的Sylvester-Gallai定理的一种变体（代数曲线为第三级）：如果在$ \ Mathbb {r}^2中没有足够多点的有限集包含在立方体中，那么有一个立方体包含确切的观点。这解决了1988年怀斯曼和威尔逊的猜想的第一个未知案例，他们证明了西尔维斯特·甘莱（Sylvester-Gallai）的变体用于圆锥形，并猜想对任何程度的曲线都有类似的陈述。
We prove a variant of the Sylvester-Gallai theorem for cubics (algebraic curves of degree three): If a finite set of sufficiently many points in $\mathbb{R}^2$ is not contained in a cubic, then there is a cubic that contains exactly nine of the points. This resolves the first unknown case of a conjecture of Wiseman and Wilson from 1988, who proved a variant of Sylvester-Gallai for conics and conjectured that similar statements hold for curves of any degree.
