Abstract
The projective plane \(\mathbb{P}\mathbb{G}(2,\;q^2 )\) is embedded as a variety of projective points\(\mathcal{V}\) in \(\mathbb{P}\mathbb{G}(M)\), where M is a nine dimensional \(\mathbb{F}_q \)-module for the groupG=GL(3,q 2). The hyperplane sections of thisvariety and their stabilizers in the group G aredetermined. When q ≡ 2 (mod 3) one such hyperplanesection is a member of the family of Kantor's unitary ovoids.We furtherdetermine all sections \(\mathbb{P}\mathbb{G}(D)\; \cap \mathcal{V}\) whereD has codimension two in M and demonstratethat these are never empty. Consequences are drawn for Kantor'sovoids.
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Cooperstein, B.N. Hyperplane Sections of Kantor's Unitary Ovoids. Designs, Codes and Cryptography 23, 185–196 (2001). https://doi.org/10.1023/A:1011264632630
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DOI: https://doi.org/10.1023/A:1011264632630