直线与反对在例外型李 incidence 几何中的研究
Lines and Opposition in Lie Incidence Geometries of Exceptional Type
AI总结：
本文研究了例外型李 incidence 几何中直线的性质，通过反对关系定义几何线，并将其与最小阻挡集联系起来。
摘要：
我们刻画了例外型李 incidence 几何中点集的性质，即从例外类型球面建筑中自然产生的几何，这些点集通过反对关系形成一条线。借此，我们对这些几何中的许多几何线进行了分类。此外，我们的结果导致了在有限例外型李 incidence 几何中几何线的刻画作为最小阻挡集，即大小为线的点集，其成员没有对象与之相反，在大多数情况下，我们还分类了所有例外情况。作为进一步的结果，我们获得了例外球面建筑的自同构作为某些保持反对关系的映射的刻画。
英文摘要：
We characterise sets of points of exceptional Lie incidence geometries, that is, the natural geometries arising from spherical buildings of exceptional types $\mathsf{F_4}$, $\mathsf{E_6}$, $\mathsf{E_7}$, $\mathsf{E_8}$ and $\mathsf{G_2}$, that form a line using the opposition relation. With that, we obtain a classification of so-called ``geometric lines'' in many of these geometries. Furthermore, our results lead to a characterisation of geometric lines in finite exceptional Lie incidence geometries as minimal blocking sets, that is, point sets of the size of a line admitting no object opposite to all of their members, in most cases, and we classify all exceptions. As a further consequence, we obtain a characterisation of automorphisms of exceptional spherical buildings as certain opposition preserving maps.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
