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

Abstract

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

9 pages