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Representation of quasiregular configurations. (Russian. English summary) Zbl 0731.51003

This paper continues the work by the first of the authors [Rend. Ist. Mat. Univ. Trieste 2, 139-145 (1970; Zbl 0213.220)] concerning the representations of free projective planes in the three-dimensional projective space. Here the focus is on finite quasiregular configurations and the following two main results are proved: (1) Any quasi-regular configuration \({\mathcal K}\) is representable in the three-dimensional projective space \(\pi_ 3(F)\) over a field F of characteristic 0, and (2) any quasiregular configuration \({\mathcal K}\) that is locally representable in a Desarguesian plane is representable in the projective plane \(\pi_ 2(F)\) over an algebraically closed field F of characteristic 0, as well.
Reviewer: J.Libicher (Brno)

MSC:

51A30 Desarguesian and Pappian geometries
51A45 Incidence structures embeddable into projective geometries
05B30 Other designs, configurations
51E14 Finite partial geometries (general), nets, partial spreads

Citations:

Zbl 0213.220
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