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

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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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Official URL: http://dx.doi.org/10.1007/s00022-020-00548-1


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
ID Code:40130
Deposited By:Michel Lavrauw
Deposited On:15 Sep 2020 19:10
Last Modified:15 Sep 2020 19:10

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