On characteristic configurations of point correspondences between spaces: Algebraic aspect (cubic \(\omega\)-systems) (Q2719505)

The paper deals with two projective spaces \(P_n\) and \(P_n'\) attributed to the arbitrary chosen systems of affine coordinates \(u^i\) and \(x^j\) \((i,j=1,2,\dots,n)\) respectively. The author develops some ideas of his paper [Vestn. Ross. Univ. Druzh. Nar., Ser. Mat. 3, No. 2, 86-98 (1996; Zbl 0970.51019)]. Namely, similarly to the eigenvector for the rectangular matrix \((3\times 6)\) the notion of semi-eigenvector is introduced which is adequate to the notion of characteristic direction of the point correspondence between the spaces. The introduced notion is applied to classify the characteristic configurations and to construct the cubic \(\omega\)-systems.