On the Hermitian Veronesean

TL;DR

This paper provides new local characterizations of the Hermitian Veronesean in projective geometry, focusing on sublines and point perspectives, enhancing understanding of its geometric properties.

Contribution

It introduces two novel local characterizations of the Hermitian Veronesean based on sublines and triples of points in perspective.

Findings

New local characterizations of the Hermitian Veronesean

Characterizations based on sublines and point perspectives

Enhanced understanding of the geometric structure

Abstract

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