On ovoids of PG(3, q)
نویسنده
چکیده
We give necessary and sufficient conditions that a polynomial f(x, y) gives an ovoid of PG(3, q). Furthermore by considering Rédei polynomials associated to ovoids of PG(3, q) we obtain sets of equations relating the coefficients of f(x, y). One such set of equations implies that if xy occurs as a term in f(x, y) + xy then i and j must have disjoint binary expansions.
منابع مشابه
Group–theoretic characterizations of classical ovoids
An ovoid of PG(3, q), q > 2, is a set of q + 1 points of PG(3, q), no three of which are collinear. The only known ovoids of PG(3, q) are the elliptic quadrics, which exist for all q, and the Suzuki-Tits ovoids, which exist for q = 2, e ≥ 3 odd, [10]. It is well known that for odd q, the only ovoids are the elliptic quadrics. For even q, the ovoids have been classified only for q up to and incl...
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