Characterising elliptic solids of Q(4, q), q even

被引：3
|
作者：
Barwick, S. G. [1 ]
Hui, Alice M. W. [2 ]
Jackson, Wen-Ai [1 ]
机构：
[1] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia
[2] BNU HKBU United Int Coll, Stat Program, Zhuhai, Peoples R China
来源：
DISCRETE MATHEMATICS | 2020年 / 343卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Projective geometry; Quadrics; Hyperplanes; SETS;
D O I：
10.1016/j.disc.2020.111857
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let epsilon be a set of solids (hyperplanes) in PG(4, q), q even, q > 2, such that every point of PG(4, q) lies in either 0, 1/2 (q(3) - q(2)) or 1/2 q(3) solids of epsilon, and every plane of PG(4, q) lies in either 0, 1/2q or q solids of epsilon. This article shows that epsilon is either the set of solids that are disjoint from a hyperoval, or the set of solids that meet a non-singular quadric Q(4, q) in an elliptic quadric. Crown Copyright (C) 2020 Published by Elsevier B.V. All rights reserved.
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