English

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

Combinatorics 2023-06-05 v1

Abstract

We prove that, if qq is large enough, the set of the Fq6\mathbb{F}_{q^6}-rational points of the Hermitian curve is a complete (q+1)(q+1)-arc in PG(2,Fq6)\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.

Keywords

Cite

@article{arxiv.2306.01134,
  title  = {Complete $(q+1)$-arcs in $\mathrm{PG}(2,\mathbb{F}_{q^6})$ from the Hermitian curve},
  author = {Daniele Bartoli and Marco Timpanella},
  journal= {arXiv preprint arXiv:2306.01134},
  year   = {2023}
}