Nets of conics of rank one in PG(2, q), q odd

被引：0

作者：

Lavrauw, Michel ^{[1
]}

Popiel, Tomasz ^{[2
]}

Sheekey, John ^{[3
]}

机构：

[1] Sabanci Univ, Istanbul, Turkey

[2] Queen Mary Univ London, London, England

[3] Univ Coll Dublin, Dublin, Ireland

来源：

JOURNAL OF GEOMETRY | 2020年 / 111卷 / 03期

关键词：

FIELDS;

D O I：

10.1007/s00022-020-00548-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify nets of conics of rank one in Desarguesian projective planes over finite fields of odd order, namely, two-dimensional linear systems of conics containing a repeated line. Our proof is geometric in the sense that we solve the equivalent problem of classifying the orbits of planes in PG(5, q) which meet the quadric Veronesean in at least one point, under the action of PGL(3, q) <= PGL(6, q) (for q odd). Our results complete a partial classification of nets of conics of rank one obtained by Wilson (Am J Math 36:187-210, 1914).

引用

页数：35

共 50 条

[41] ON NETS OF ORDER Q(2) AND DEGREE Q+1 ADMITTING GL(2, Q)
HIRAMINE, Y
GEOMETRIAE DEDICATA, 1993, 48 (02) : 139 - 189
[42] A characterization of the family of external lines to a quadratic cone of PG(3, q), q odd
Di Gennaro R.
Durante N.
Olanda D.
Journal of Geometry, 2009, 96 (1-2) : 63 - 70
[43] A characterization of the family of secant lines to a hyperbolic quadric in PG(3, q), q odd
Pradhan, Puspendu
Sahu, Bikramaditya
DISCRETE MATHEMATICS, 2020, 343 (11)
[44] THE AFFINE PLANE AG(2,Q), Q-ODD, HAS A UNIQUE ONE-POINT EXTENSION
THAS, JA
INVENTIONES MATHEMATICAE, 1994, 118 (01) : 133 - 139
[45] On (q2 + q + 2, q + 2)-arcs in the Projective Plane PG(2, q)
Simeon Ball
Ray Hill
Ivan Landjev
Harold Ward
Designs, Codes and Cryptography, 2001, 24 : 205 - 224
[46] Infinite family of large complete arcs in PG(2, qn), with q odd and n > 1 odd
Gábor Korchmáros
Nicola Pace
Designs, Codes and Cryptography, 2010, 55 : 285 - 296
[47] SET OF GENERATORS AND RELATIONS FOR GROUP PSL(2,Q), Q ODD
BEETHAM, MJ
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1971, 3 (APR): : 554 - &
[48] THE 2-DECOMPOSITION NUMBERS OF SP(4, Q), Q ODD
WHITE, DL
JOURNAL OF ALGEBRA, 1990, 131 (02) : 703 - 725
[49] A group theoretic characterization of Buekenhout-Metz unitals in PG(2, q2) containing conics
Donati, Giorgio
Durante, Nicola
DISCRETE MATHEMATICS, 2012, 312 (15) : 2371 - 2374
[50] Minimal blocking sets of size q2+2 of Q(4, q), q an odd prime, do not exist
De Beule, J
Metsch, K
FINITE FIELDS AND THEIR APPLICATIONS, 2005, 11 (02) : 305 - 315

← 1 2 3 4 5 →