论文标题
关于Q的低度卵形的分类（4，Q）
On the classification of low-degree ovoids of Q(4,q)
论文作者
论文摘要
自80年代结束以来，已经研究了PG（4，Q）的非分类二次Q（4，Q）的卵形。它们是罕见的对象，除了椭圆四边形给出的经典示例外，只有三类以q奇数为名，一个类别为$ q $的类别，以及一个零星的示例，以$ q = 3^5。众所周知，对于Q（4，Q）的任何卵形，双变量多项式F（x，y）都可以关联。在本文中，我们对Q（4，q）的卵形进行分类，其相应的多项式F（x，y）与Q相比具有“低度”，尤其是deg（f）<（q/6.3）^（3/13）-1。最后，作为一个应用程序，获得了特征3中的置换多项式的{两类}。
Ovoids of the non-degenerate quadric Q(4,q) of PG(4,q) have been studied since the end of the '80s. They are rare objects and, beside the classical example given by an elliptic quadric, only three classes are known for q odd, one class for $q$ even, and a sporadic example for $ìq=3^5. It is well known that to any ovoid of Q(4,q) a bivariate polynomial f(x,y) can be associated. In this paper we classify ovoids of Q(4,q) whose corresponding polynomial f(x,y) has 'low degree' compared with q, in particular deg(f)<(q/6.3)^(3/13)-1. Finally, as an application, {two classes} of permutation polynomials in characteristic 3 are obtained.
