An infinite family of m-ovoids of Q(4,q)

Abstract

In this paper, we construct an infinite family of $\frac{q-1}{2}$-ovoids of the generalized quadrangle $Q(4,q)$, for $q\equiv 1(\text{mod}4)$ and $q>5$. Together with [3] and [11], this establishes the existence of $\frac{q-1}{2}$-ovoids in $Q(4,q)$ for each odd prime power q.