Hyperovals of $H(3,q^2)$ when $q$ is even

Antonio Cossidente, Oliver H. King, Giuseppe Marino

For even $q$, a group $G$ isomorphic to $PSL(2,q)$ stabilizes a Baer conic inside a symplectic subquadrangle $\mathcal{W}(3,q)$ of $\mathcal{H}(3,q^2)$. In this paper the action of $G$ o…