Ovoids in the cyclic presentation of PG(3,q)

2024/10/05 by Kanat Abdukhalikov, Simeon Ball, Abdukhalikov, Kanat +5
Engineering · Mathematics · #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2410.04126

openalex publication_date 2024/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the cyclic presentation of PG(3,q) whose points are in the finite field \mathbbF_q⁴ and describe the known ovoids therein. We revisit the set O, consisting of (q²+1)-th roots of unity in \mathbbF_q⁴, and prove that it forms an elliptic quadric within the cyclic presentation of PG(3,q). Additionally, following the work of Glauberman on Suzuki groups, we offer a new description of Suzuki-Tits ovoids in the cyclic presentation of PG(3,q), characterizing them as the zeroes of a polynomial over \mathbbF_q⁴.

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