Ovoids of Q(6, q) of low degree

Abstract Ovoids of the parabolic quadric Q (6, q) of PG (6, q) PG (6, q) have been largely studied in the last 40 years. They can only occur if q is an odd prime power and there are two known families of ovoids of Q (6, q), the Thas-Kantor ovoids and the Ree-Tits ovoids, both for q a power of 3. It is well known that to any ovoid of Q (6, q) two polynomials f₁ (X, Y, Z) f 1 (X, Y, Z), f₂ (X, Y, Z) f 2 (X, Y, Z) can be associated. In this paper we classify ovoids of Q (6, q) with \ (f₁), (f₂) \ max deg (f 1), deg (f 2) (1 6. 3 q) 3 13 - 1.