Locally hermitian partial ovoids of unitary polar spaces and partial ovoids of orthogonal polar spaces (Q1022881)

The author studies the Barlotti-Cofman representation of the unitary polar spaces \(H(n,q^{2})\) for all \(n\) and he proves that to any locally hermitian partial ovoid of such spaces corresponds a partial ovoid of an orthogonal polar space, and conversely. Further the locally hermitian partial ovoid is maximal if and only if the corresponding partial ovoid of the orthogonal polar space is maximal. Also, the author gives a geometric proof to derive that the orthogonal polar space \(Q^{+}(4n+1,q)\) has no ovoid when \(n>q^{3}\).