论文标题
pg中二次锥体羊群的分类（3,64）
Classification of flocks of the quadratic cone in PG(3,64)
论文作者
论文摘要
羊群是有限几何学领域的重要话题，与其他感兴趣的对象有许多关系。本文是对将羊群分类为投影对等的困难问题的贡献。我们通过计算机通过计算机表明pg（3,64）中恰好有三个二次锥体的鸡群（3,64），以q <= 71的pg（3，q）中的二次锥体的分类（q <= 71）完成。以前已经发现了这三只羊群，它们是线性羊群，亚基亚群羊群和阿德莱德羊群。分类通过pg（2，q），q偶数的卵子和椭圆形群之间的连接进行进行进行，并使用PG中的超伏的先前分类（2,64）。
Flocks are an important topic in the field of finite geometry, with many relations with other objects of interest. This paper is a contribution to the difficult problem of classifying flocks up to projective equivalence. We complete the classification of flocks of the quadratic cone in PG(3,q) for q <= 71, by showing by computer that there are exactly three flocks of the quadratic cone in PG(3,64), up to equivalence. The three flocks had previously been discovered, and they are the linear flock, the Subiaco flock and the Adelaide flock. The classification proceeds via the connection between flocks and herds of ovals in PG(2,q), q even, and uses the prior classification of hyperovals in PG(2,64).
