关于有限典型极空间的正则系
On regular systems of finite classical polar spaces
摘要：
设$\cal P$是秩为$d$的有限经典极空间.关于$\cal P$的$(k - 1)$ -维射影空间的$m$ -正则系统，$1 \le k \le d - 1$，是$\cal P$的生成元的集合$\cal R$，其性质是$\cal P$的每个$(k - 1)$ -维射影空间恰好位于$\cal R$的$m$生成元上.研究了极空间的正则系统。证明了某些低秩极空间的1-正则系统的不存在性，并给出了由给定的$m$ -正则系统得到$m'$-正则系统的方法.最后，给出了正则系统的三种不同构造方法。讨论了各种极空间的点。
英文摘要：
Let $\cal P$ be a finite classical polar space of rank $d$. An $m$-regular system with respect to $(k - 1)$-dimensional projective spaces of $\cal P$, $1 \le k \le d - 1$, is a set $\cal R$ of generators of $\cal P$ with the property that every $(k - 1)$-dimensional projective space of $\cal P$ lies on exactly $m$ generators of $\cal R$. Regular systems of polar spaces are investigated. Some non-existence results about certain 1-regular systems of polar spaces with low rank are proved and a procedure to obtain $m'$-regular systems from a given $m$-regular system is described. Finally, three different construction methods of regular systems w.r.t. points of various polar spaces are discussed.
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