Orbits and incidence matrices for points, planes and lines regarding the twisted cubic in PG(3,q), q = 2, 3, 4
Abstract
In the three-dimensional projective space PG(3,q) over the finite field Fq with q elements, we consider the normal rational curve known as a twisted cubic and the projectivity group Gq that fixes it. For q = 2, 3, 4, we solve the open problems of classifying the orbits of points, planes, and lines under Gq and of determining the corresponding incidence matrices between points, planes, and lines partitioned into these orbits.
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