2025/02/04 by Daniele Bartoli, Nicola Durante, Bartoli, Daniele +5
Computer Science · Mathematics · #05B25 #11T06 #51E20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2502.02219
openalex publication_date 2025/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Ovoids of the hyperbolic quadric Q+(7,q) of PG(7,q) have been extensively studied over the past 40 years, partly due to their connections with other combinatorial objects. It is well known that the points of an ovoid of Q+(7,q) can be parametrized by three polynomials f1(X,Y,Z), f2(X,Y,Z), f3(X,Y,Z). In this paper, we classify ovoids of Q+(7,q) of low degree, specifically under the assumption that f1(X,Y,Z), f2(X,Y,Z), f3(X,Y,Z) have degree at most 3. Our approach relies on the analysis of an algebraic hypersurface associated with the ovoid.