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

13 Mar 2020 Lavrauw Michel Popiel Tomasz Sheekey John

We classify nets of conics 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 $\text{PG}(5,q)$ which meet the quadric Veronesean in at least one point, under the action of $\text{PGL}(3,q) \leqslant \text{PGL}(6,q)$ (for $q$ odd)... (read more)

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• COMBINATORICS
• ALGEBRAIC GEOMETRY