有限射影空间中的蛋与平移平面中的么正
Eggs in finite projective spaces and unitals in translation planes
摘要：
受卵形体和酉单位之间的联系的启发，从Buekenhout结构中产生的André/Bruck-Bose表示的平移平面的最多2个在其内核上，因为PG（4 m-1，q），m>=1的鸡蛋，是卵形体的推广，我们探讨鸡蛋和酉单位之间的关系，在其内核上的更高维度的平移平面。通过研究这种关系，我们在3^{10}阶Dickson半场平面上构造了一个么正，它在PG（20，3）中用一个锥表示，该锥的底是PG（19，3）中Penttila-Williams蛋的对偶点的集合。这个单位元不是极性的，因此，据作者所知，它似乎是这样一个平面上的一个新单位元。
英文摘要：
Inspired by the connection between ovoids and unitals arising from the Buekenhout construction in the André/Bruck-Bose representation of translation planes of dimension at most two over their kernel, and since eggs of PG(4m-1,q), m>=1, are a generalization of ovoids, we explore the relation between eggs and unitals in translation planes of higher dimension over their kernel. By investigating such a relationship, we construct a unital in the Dickson semifield plane of order 3^{10}, which is represented in PG(20,3) by a cone whose base is a set of points constructed from the dual of the Penttila-Williams egg in PG(19,3). This unital is not polar; so, up to the knowledge of the authors, it seems to be a new unital in such a plane.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
