Blocking sets of tangent lines to a hyperbolic quadric in PG(3,3)

被引：5

作者：

De Bruyn, Bart ^{[1
]}

Sahoo, Binod Kumar ^{[2
]}

Sahu, Bikramaditya ^{[2
]}

机构：

[1] Univ Ghent, Dept Math Algebra & Geometry, Krijgslaan 281 S22, B-9000 Ghent, Belgium

[2] Natl Inst Sci Educ & Res, HBNI, Sch Math Sci, PO Jatni, Bhubaneswar 752050, Odisha, India

来源：

DISCRETE APPLIED MATHEMATICS | 2019年 / 266卷

关键词：

Projective space; Blocking set; Conic; Ovoid; Hyperbolic quadric;

D O I：

10.1016/j.dam.2018.12.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Q(+)(3, q) be a hyperbolic quadric in PG(3, q) and T be the set of all lines of PG(3, q) which are tangent to Q(+)(3, q). If k is the minimum size of a T-blocking set in PG(3, q), then we prove that q(2) + 1 <= k <= q(2) + q. When q = 3, we show that: (i) there is no T-blocking set of size 10, and (ii) there are exactly two T-blocking sets of size 11 up to isomorphism. By means of the computer algebra systems GAP (The GAP Group, 2014) and Sage (Sage Mathematics Software (Version 6.3), 2014), we find that there exist no T-blocking sets of size q(2) + 1 for each odd prime power q <= 13. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：121 / 129

页数：9

共 47 条

[41] Further Results on Orbits and Incidence Matrices for the Class O6 of Lines External to the Twisted Cubic in PG(3,q) [J].

Davydov, Alexander A. ;

Marcugini, Stefano ;

Pambianco, Fernanda .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2025, 22 (05)

[42] Orbits of Lines for a Twisted Cubic in PG(3,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textrm{PG}(3,q)$$\end{document} [J].

Alexander A. Davydov ;

Stefano Marcugini ;

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Mediterranean Journal of Mathematics, 2023, 20 (3)

[43] Ruled sets of plane–type (m,h)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{(m, h)_2}$$\end{document} in PG(3,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{PG}\varvec{(3, q)}$$\end{document} with m≤q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{m\le q}$$\end{document} [J].

Vito Napolitano .

Journal of Geometry, 2017, 108 (3) :953-960

[44] Two characterizations of the family of secant lines of an ovoid of PG(3, q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{q}}$$\end{document}) [J].

Vito Napolitano .

Journal of Geometry, 2019, 110 (2)

[45] Orbits of the Class O6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {O}}_6$$\end{document} of Lines External to the Twisted Cubic in PG(3,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textrm{PG}(3,q)$$\end{document} [J].

Alexander A. Davydov ;

Stefano Marcugini ;

Fernanda Pambianco .

Mediterranean Journal of Mathematics, 2023, 20 (3)

[46] Incidence matrices for the class O6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {O}}_6$$\end{document} of lines external to the twisted cubic in PG(3,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textrm{PG}(3,q)$$\end{document} [J].

Alexander A. Davydov ;

Stefano Marcugini ;

Fernanda Pambianco .

Journal of Geometry, 2023, 114 (2)

[47] On sets of plane-type (0,mq,2mq)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(0, mq, 2mq)_2$$\end{document} in PG(3,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {PG}(3, q)$$\end{document} with a long secant [J].

Vito Napolitano .

Journal of Geometry, 2020, 111 (3)

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