We prove that, if q is large enough, the set of the Fq6-rational points of the Hermitian curve is a complete (q6+q5-q4+1,q+1)-arc in PG(2,Fq6), 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.
Complete $$(k,q+1)$$-arcs in $$\textrm{PG}(2,\mathbb {F}_{q^6})$$ from the Hermitian curve
Bartoli, Daniele;Timpanella, Marco
2025
Abstract
We prove that, if q is large enough, the set of the Fq6-rational points of the Hermitian curve is a complete (q6+q5-q4+1,q+1)-arc in PG(2,Fq6), 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.File in questo prodotto:
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