论文标题
基于线性套件的ABB占用
A higgledy-piggledy set of planes based on the ABB-representation of linear sets
论文作者
论文摘要
在本文中，我们调查了某些$ \ mathbb {f} _q $ - 线性集的André/bruck-bose表示，包含在$ \ text {pg}（2，q^t）$的行中。我们表明，零散的$ \ mathbb {f} _q $ - 等级的$ 3 $ in $ \ text {pg}（1，q^3）$对应于特定的超纤维四边形，该$ \ mathbb {f} f} _q $ linear linarear linear linear clubs in $ \ \ text $ \ \ text $ - 在正常的有理曲线上；该设计扩展了围绕圆锥形的束缚的概念。最后，我们使用这些结果来构建$ \ text {pg}（5，q）$的最佳higgledy-piggledy套装。
In this paper, we investigate the André/Bruck-Bose representation of certain $\mathbb{F}_q$-linear sets contained in a line of $\text{PG}(2,q^t)$. We show that scattered $\mathbb{F}_q$-linear sets of rank $3$ in $\text{PG}(1,q^3)$ correspond to particular hyperbolic quadrics and that $\mathbb{F}_q$-linear clubs in $\text{PG}(1,q^t)$ are linked to subspaces of a certain $2$-design based on normal rational curves; this design extends the notion of a circumscribed bundle of conics. Finally, we use these results to construct optimal higgledy-piggledy sets of planes in $\text{PG}(5,q)$.
