Baer子平面上的二次曲线
Conics in Baer subplanes
摘要：
本文研究了$PG(2,q^2)$的二次曲线和次曲线及其在$PG(4,q)$中André/Bruck-Bose环境下的表示.特别是，我们调查他们的关系与横向线的定期蔓延。主要结果是表明，在$PG(2,q^2)$的切线Baer子平面中的二次曲线在$PG(4,q)$中对应于与规则展开的横向线相交的法向有理曲线。相反地，$PG(4,q)$中的每一条与规则展度的横线相交的3维和4维正规有理曲线对应于$PG(2,q^2)$的切线Baer子平面中的二次曲线。
英文摘要：
This article studies conics and subconics of $PG(2,q^2)$ and their representation in the André/Bruck-Bose setting in $PG(4,q)$. In particular, we investigate their relationship with the transversal lines of the regular spread. The main result is to show that a conic in a tangent Baer subplane of $PG(2,q^2)$ corresponds in $PG(4,q)$ to a normal rational curve that meets the transversal lines of the regular spread. Conversely, every 3 and 4-dimensional normal rational curve in $PG(4,q)$ that meets the transversal lines of the regular spread corresponds to a conic in a tangent Baer subplane of $PG(2,q^2)$.
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。
