An infinite family of $m$-ovoids of the hyperbolic quadrics $\mathcal{Q}^+(7,q)$

TL;DR

This paper constructs an infinite family of large $m$-ovoids in hyperbolic quadrics $ ext{Q}^+(7,q)$ for certain q, using generalized hexagon theory, expanding understanding of geometric structures in finite projective spaces.

Contribution

It introduces a new infinite family of $m$-ovoids in $ ext{Q}^+(7,q)$ for $q ot ot ext{congruent to } 1 ext{ mod } 3$, utilizing the theory of generalized hexagons.

Findings

Constructed an infinite family of $(q^2+q+1)$-ovoids for $q ot ot ext{congruent to } 1 ext{ mod } 3$.

The group $ ext{PGL}(3,q)$ acts on these $m$-ovoids.

Utilized the theory of generalized hexagons to achieve the construction.

Abstract

An infinite family of $(q^2+q+1)$-ovoids of $\mathcal{Q}^+(7,q)$, $q\equiv 1\pmod{3}$, admitting the group $\mathrm{PGL}(3,q)$, is constructed. The main tool is the general theory of generalized hexagons.