On the Hermitian Veronesean

Published 9 May 2025 in math.CO | (2505.05827v1)

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.

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