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Ovoid (projective geometry)
From Wikipedia, the free encyclopedia
In PG(3,q), with q a prime power, an ovoid is a set of q2 + 1 points, no three of which collinear.
An important example of an ovoid in any finite projective three-dimensional space are the q2 + 1 points of an elliptic quadric (all of these are projectively equivalent).
When q is odd, no other ovoids can be found than the elliptic quadrics.
When q = 22h + 1 another type of ovoid can be constructed : the Tits ovoid or also the Suzuki ovoid. It is conjectured that no other ovoids exist in PG(3,q).
Through every point p on the ovoid, there are exactly q + 1 tangents, and it can be proven that these lines are exactly the lines through p in one specific plane through p. This means that through every point p in the ovoid, there is a unique plane intersecting the ovoid in exactly one point.