Abstract
We show that a non-degenerate Hermitian variety \({\mathcal{H}(2n, q^2)}\) in PG(2n, q2) can be partitioned in Baer parabolic quadrics Q(2n, q), if q is odd, or in Baer symplectic spaces \({\mathcal{W}(2n-1, q)}\) , if q is even. We construct a partial spread of \({\mathcal{H}(4, q^2)}\) of size (q5 + 1)/(q + 1), admitting a group of order (q5 + 1)/(q + 1) and a hyperoval of size 2(q5 + 1)/(q + 1) on \({\mathcal{DH}(4, q^2)}\) , the point line dual generalized quadrangle of \({\mathcal{H}(4, q^2)}\) , admitting a dihedral group of order 2(q5 + 1)/(q + 1).
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