论文标题
关于凯利（Kelly
On a Conjecture of Kelly on $(1,3)$-representation of Sylvester Gallai Designs
论文作者
论文摘要
我们给出了L.M. Kelly的猜想的确切标准，以保持真实，如下所示。如果有一个有限的家庭$σ$的相互偏度线中的$ \ mathbb {r}^l，l \ geq 4 $，以至于每两行的三维仿射跨度（hull）中的$σ$中的三个维度跨度（hull）至少包含$σ$的一行，那么我们就有一个$σ$完全包含在三个尺寸的空间中，并且仅包含hif hif hif and。最后，本文为更高维偏度的仿射空间提出了一个类似的问题，即$（2,5）$ - 以$ \ mathbb {r}^6 $的形式表示sylvester-gallai设计的表示，这是在最后一部分中回答的。
We give an exact criterion of a conjecture of L.M.Kelly to hold true which is stated as follows. If there is a finite family $Σ$ of mutually skew lines in $\mathbb{R}^l,l\geq 4$ such that the three dimensional affine span (hull) of every two lines in $Σ$, contains at least one more line of $Σ$, then we have that $Σ$ is entirely contained in a three dimensional space if and only if the arrangement of affine hulls is central. Finally, this article leads to an analogous question for higher dimensional skew affine spaces, that is, for $(2,5)$-representations of sylvester-gallai designs in $\mathbb{R}^6$, which is answered in the last section.
