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 \((q^6+q^5-q^4+1,q+1)\) -arc in \(\textrm{PG}(2,\mathbb {F}_{q^6})\) , addressing an open case from a recent paper by Korchmáros et al. (J Comb Theory Ser A 204:105851, 2024). An algebraic approach based on the investigation of some algebraic varieties attached to the arc is used.
