1. Ovoids of $Q^+(7,q)$ of low-degree
- Author
-
Bartoli, Daniele, Durante, Nicola, Grimaldi, Giovanni Giuseppe, and Timpanella, Marco
- Subjects
Mathematics - Combinatorics ,Mathematics - Algebraic Geometry ,05B25, 11T06, 51E20 - Abstract
Ovoids of the hyperbolic quadric $Q^+(7,q)$ of $\mathrm{PG}(7,q)$ 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 $f_1(X,Y,Z)$, $f_2(X,Y,Z)$, $f_3(X,Y,Z)$. In this paper, we classify ovoids of $Q^+(7,q)$ of low degree, specifically under the assumption that $f_1(X,Y,Z)$, $f_2(X,Y,Z)$, $f_3(X,Y,Z)$ have degree at most 3. Our approach relies on the analysis of an algebraic hypersurface associated with the ovoid.
- Published
- 2025