Ovoids of the parabolic quadric Q(6, q) of \(\textrm{PG}(6,q)\) 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 \(f_1(X,Y,Z)\), \(f_2(X,Y,Z)\) can be associated. In this paper we classify ovoids of Q(6, q) with \(\max \{\deg (f_1),\deg (f_2)\}<(\frac{1}{6.3}q)^{\frac{3}{13}}-1\).

中文翻译：

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低阶 Q(6, q) 的卵形

\(\textrm{PG}(6,q)\)的抛物线二次曲面Q (6  , q )的卵形在过去 40 年得到了广泛的研究。它们只有在q是奇素数幂且有两个已知的Q (6,  q ) 卵形体家族（Thas-Kantor 卵形体和 Ree-Tits 卵形体）时才会出现，两者都为q的 3 次幂。已知对于Q (6,  q ) 的任何卵形，两个多项式\(f_1(X,Y,Z)\)、\(f_2(X,Y,Z)\)可以关联。在本文中，我们对Q (6,  q )的卵形进行分类： \(\max \{\deg (f_1),\deg (f_2)\}<(\frac{1}{6.3}q)^{\frac{ 3}{13}}-1\)。