%0 Journal Article
%T Hyperovals of $H(3,q^2)$ when $q$ is even
%A Antonio Cossidente
%A Oliver H. King
%A Giuseppe Marino
%J Mathematics
%D 2012
%I arXiv
%X For even $q$, a group $G$ isomorphic to $PSL(2,q)$ stabilizes a Baer conic inside a symplectic subquadrangle ${\cal W}(3,q)$ of ${\cal H}(3,q^2)$. In this paper the action of $G$ on points and lines of ${\cal H}(3,q^2)$ is investigated. A construction is given of an infinite family of hyperovals of size $2(q^3-q)$ of ${\cal H}(3,q^2)$, with each hyperoval having the property that its automorphism group contains $G$. Finally it is shown that the hyperovals constructed are not isomorphic to known hyperovals.
%U http://arxiv.org/abs/1211.3649v1