论文标题
经典极性空间的几乎所有子空间都来自其通用嵌入
Nearly all subspaces of a classical polar space arise from its universal embedding
论文作者
论文摘要
令$γ$为有限等级$ n \ geq 2 $的可嵌入的非分类极性空间。假设$γ$承认通用嵌入（对于所有可嵌入的极性空间都是正确的，除了至少$ 5 $的订单网格和在Quaternion diseconter戒指上定义的某些通用四边形），请让$ \ varepsilon：γ\ to \ mathrm {pg}（v）$是$ umperding of $γ$。令$ \ cal s $为$γ$的子空间，假设被视为极性空间的$ \ cal s $至少$ 2 $。我们将证明$ \ cal s $是$ \ varepsilon $ -primage $ \ mathrm {pg}（v）$的投影子空间。
Let $Γ$ be an embeddable non-degenerate polar space of finite rank $n \geq 2$. Assuming that $Γ$ admits the universal embedding (which is true for all embeddable polar spaces except grids of order at least $5$ and certain generalized quadrangles defined over quaternion division rings), let $\varepsilon:Γ\to\mathrm{PG}(V)$ be the universal embedding of $Γ$. Let $\cal S$ be a subspace of $Γ$ and suppose that $\cal S$, regarded as a polar space, has non-degenerate rank at least $2$. We shall prove that $\cal S$ is the $\varepsilon$-preimage of a projective subspace of $\mathrm{PG}(V)$.
