The classification of subplane covered nets. (English) Zbl 0855.51002

A net is called subplane covered if for any two distinct collinear points there is a subplane which contains the two points and whose infinite points are the infinite points of the net. Extending his results on the structure of derivable nets, the author proves that every subplane covered net can be obtained from a projective space \(\Sigma\) and a subspace \(N\) of codimension 2 as follows. Points of the net are the lines of \(\Sigma\) which do not intersect \(N\) and lines of the net are the points of \(\Sigma\) not contained in \(N\). The subplanes of the net correspond to the subplanes of \(\Sigma\) which intersect \(N\) in precisely one point.


51A15 Linear incidence geometric structures with parallelism
51A45 Incidence structures embeddable into projective geometries
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