Abstract
It is shown that if a spread of a finite split Cayley hexagon is translation with respect to two disjoint flags then it is either a hermitian spread or a Ree–Tits spread. Analogously, if an ovoid of a classical generalized quadrangle Q(4, q) is translation with respect to two disjoint flags then it is either an elliptic quadric or a Suzuki–Tits ovoid. In the course of obtaining these results, we introduce the notion of local polarity for ovoid-spread pairings and show that if an ovoid-spread pairing is locally polar at each of its elements then it arises from a polarity.
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Offer, A., Maldeghem, H.V. Spreads and Ovoids Translation with Respect to Disjoint Flags. Designs, Codes and Cryptography 32, 351–367 (2004). https://doi.org/10.1023/B:DESI.0000029234.00193.60
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DOI: https://doi.org/10.1023/B:DESI.0000029234.00193.60