On m-ovoids of Q+(7, q) with q odd

被引：0
|
作者：
Adriaensen, Sam [1 ]
De Beule, Jan [1 ]
Grimaldi, Giovanni Giuseppe [2 ]
Mannaert, Jonathan [1 ]
机构：
[1] Vrije Univ Brussel, Dept Math & Data Sci, B-1050 Brussels, Belgium
[2] Univ Naples Federico II, Dept Math & Applicat R Caccioppoli, Naples, Italy
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2024年 / 95卷
关键词：
m-ovoid; Polar space; 1-SYSTEMS;
D O I：
10.1016/j.ffa.2024.102387
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we provide a construction of (q + 1) -ovoids of the hyperbolic quadric Q+(7, q), q an odd prime power, by glueing (q + 1)/2 -ovoids of the elliptic quadric Q-(5, q). This is possible by controlling some intersection properties of (putative) m -ovoids of elliptic quadrics. It eventually yields (q + 1) -ovoids of Q+(7, q) not coming from a 1 -system. Secondly, for certain values of q, we construct line spreads of PG(3, q) that have as many secants to a given elliptic quadric as possible. This is then used to construct m -ovoids for m is an element of {2, 4, 6, 8, 10} in Q+(7, 3). (c) 2024 Elsevier Inc. All rights reserved.
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页数：16
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