论文标题
在PG $（2，Q^n）$中的绝对相关点上
On absolute points of correlations in PG$(2,q^n)$
论文作者
论文摘要
令$ v $为$（d+1）$ - 字段$ \ mathbb {f} $上的维矢量空间。当反身表现出色时，对$ v $的表格形式在很大程度上进行了研究，因此产生了$ d $ d $二维的投影型太空pg $（v）$的（可能是堕落的）极性。如果$ \ mathbb {f} $是$ {\ mathbb {r}} $，$ {\ mathbb {c}} $或有限firite field $ {\ mathbb {f} _ q q $在本文中，我们考虑$ v = \ mathbb {f} _ {q^n}^3 $的退化，非反射性seSquilinear形式。我们将看到，这些表格引起了Pg $（2，Q^n）$的退化相关性，其绝对积分集除了锥度（可能是退化）$ C_F^m $ seet。在最后一部分中，我们从卑诗省的巨大工作中收集了一些结果。 Kestenband关于Pg $（2，Q^n）$中相关点的集合所闻名的，该$由$ v = \ Mathbb {f} _ {q^n}^3 $的非分级，非反射sesquilinear形式引起的。
Let $V$ be a $(d+1)$-dimensional vector space over a field $\mathbb{F}$. Sesquilinear forms over $V$ have been largely studied when they are reflexive and hence give rise to a (possibly degenerate) polarity of the $d$-dimensional projective space PG$(V)$. Everything is known in this case for both degenerate and non-degenerate reflexive forms if $\mathbb{F}$ is either ${\mathbb{R}}$, ${\mathbb{C}}$ or a finite field ${\mathbb{F}}_q$. In this paper we consider degenerate, non-reflexive sesquilinear forms of $V=\mathbb{F}_{q^n}^3$. We will see that these forms give rise to degenerate correlations of PG$(2,q^n)$ whose set of absolute points are, besides cones, the (possibly degenerate) $C_F^m$-sets. In the final section we collect some results from the huge work of B.C. Kestenband regarding what is known for the set of the absolute points of correlations in PG$(2,q^n)$ induced by a non-degenerate, non-reflexive sesquilinear form of $V=\mathbb{F}_{q^n}^3$.
