English

On the Hermitian Veronesean

Combinatorics 2025-05-12 v1

Abstract

The Hermitian Veronesean in PG(3,q2)PG(3,q^2), given by V:={(1,x,xq,xq+1):xFq}{(0,0,0,1)}\mathcal{V}:=\{ (1,x,x^q,x^{q+1}):x\in\mathbb{F}_q\}\cup\{(0,0,0,1)\}, is a well-studied rational curve, and forms a {\em special} set of the Hermitian surface H(3,q2)H(3,q^2). In this paper, we give two local characterisations of the Hermitian Veronesean, based on sublines and triples of points in perspective.

Cite

@article{arxiv.2505.05827,
  title  = {On the Hermitian Veronesean},
  author = {John Bamberg and Geertrui Van de Voorde},
  journal= {arXiv preprint arXiv:2505.05827},
  year   = {2025}
}
R2 v1 2026-06-28T23:26:51.711Z