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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 froma recent paper by Korchm\'aros, Sz\H{o}nyi and Nagy. An algebraic approachbased on the investigation of some algebraic varieties attached to the arc isused.

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