Title: Complete $(q+1)$-arcs in $\mathrm{PG}(2,\mathbb{F}_{q^6})$ from the Hermitian curve Show Chinese title

Title: 完成$(q+1)$-弧在$\mathrm{PG}(2,\mathbb{F}_{q^6})$上的埃尔米特曲线

Abstract: We prove that, if $q$ is large enough, the set of the $\mathbb{F}_{q^6}$-rational points of the Hermitian curve is a complete $(q+1)$-arc in $\mathrm{PG}(2,\mathbb{F}_{q^6})$, addressing an open case from a recent paper by Korchm\'aros, Sz\H{o}nyi and Nagy. An algebraic approach based on the investigation of some algebraic varieties attached to the arc is used. Show Chinese abstract

Abstract: 我们证明，如果$q$足够大，则赫尔米特曲线的$\mathbb{F}_{q^6}$有理点集是$\mathrm{PG}(2,\mathbb{F}_{q^6})$中的一个完全$(q+1)$弧，解决了 Korchmáros、Szőnyi 和 Nagy 最近一篇论文中的一个开放问题。采用基于对与弧相关的某些代数簇进行研究的代数方法。