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

Lavrauw, Michel and Popiel, Tomasz and Sheekey, John (2020) Nets of conics of rank one in PG(2, q), q odd. Journal of Geometry, 111 (3). ISSN 0047-2468 (Print) 1420-8997 (Online)

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Abstract

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).
Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Michel Lavrauw
Date Deposited: 15 Sep 2020 19:10
Last Modified: 15 Sep 2020 19:10
URI: https://research.sabanciuniv.edu/id/eprint/40130

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