extended to even characteristic, because of the following non-quadric examples:
* For odd and the automorphism the pointset
: is an ovoid in the 3-dimensional projective space over (represented in inhomogeneous coordinates).
:Only when is the ovoid a quadric.
: is called the Tits-Suzuki-ovoid.

Criteria for an ovoid to be a quadric

An ovoidal quadric has many symmetries. In particular:
* Let be an ovoid in a projective space of dimension and a hyperplane. If the ovoid is symmetric to

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