论文标题
在等效性，稳定器和脚的脚
On the Equivalence, Stabilisers, and Feet of Buekenhout-Tits Unitals
论文作者
论文摘要
本文解决了$ pg（2，q^2）$中有关buekenhout-tits单元的许多问题，其中$ q = 2^{e+1} $和$ e \ geq 1 $。我们表明，所有Buekenhout-tits Unitals均为$ PGL $ - 等价（解决[S. Barwick和G. L.Ebert。在投影飞机上的一个开放问题。数学中的Springer专着。单位。 [N.Abarzúa，R。Pomareda和O. Vega。
This paper addresses a number of problems concerning Buekenhout-Tits unitals in $PG(2,q^2)$, where $q = 2^{e+1}$ and $e \geq 1$. We show that all Buekenhout-Tits unitals are $PGL$-equivalent (addressing an open problem in [S. Barwick and G. L. Ebert. Unitals in projective planes. Springer Monographs in Mathematics. Springer, New York, 2008.]), explicitly describe their $PΓL$-stabiliser (expanding Ebert's work in [G.L. Ebert. Buekenhout-Tits unitals. J. Algebraic. Combin. 6.2 (1997), 133-140], and show that lines meet the feet of points no on $\ell_\infty$ in at most four points. Finally, we show that feet of points not on $\ell_\infty$ are not always a $\{0,1,2,4\}$-set, in contrast to what happens for Buekenhout-Metz unitals [N. Abarzúa, R. Pomareda, and O. Vega. Feet in orthogonal-Buekenhout-Metz unitals. Adv. Geom. 18.2 (2018), 229-236].
