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.

引用

页数：16

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