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

Chvál, Viliam; Kopas, Melichar

Math. Bohem. 116, No. 2, 119-131 (1991).

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

Keywords:

real projective space; complex projective plane; representations; quasi- regular configuration

Citations:

Zbl 0213.220