On the Hermitian Veronesean

2025/05/09 by John Bamberg, Bamberg, John, Geertrui Van de Voorde +1
Mathematics · Physics and Astronomy · #05B25 #51E12 #51E20 #Advanced Algebra and Geometry #Advanced Mathematical Theories and Applications #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.05827

openalex publication_date 2025/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Arcs, Caps and Generalisations in a Finite Projective Space
• On the geometry of the Hermitian Veronese curve and its quasi-Hermitian surfaces
• Pseudo-ovals of elliptic quadrics as Delsarte designs of association schemes

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