Adjacency in generalized projective Veronese spaces
A partial linear space is an incidence structure \({\mathfrak M}\) of points and lines such that every line is incident to at least two points and any pair of points lies on at most one line. Additional conditions define connected spaces, exchange space, \(\Gamma\)-spaces, Grassmann spaces etc. Considering multisets one associates with \({\mathfrak M}\) the Veronese spaces \(V^*_k({\mathfrak M})\). The aim of this paper is to investigate an analogue of the Chow theorem for (projective) Veronese spaces. The authors find that it does not hold unconditionally: A bijection of strong subspaces of a generalized Veronese space preserving the adjacency need not to be determined by an automorphism of the underlying space. They give conditions which assure that adjacency preserving bijections of points (or lines) of a generalized Veronese space is determined by an automorphism of this space. The results are applied to Veronese spaces associated with projective structures.
generalized Veronese spaces (associated with a partial linear space)
scientific article; zbMATH DE number 5184532
scientific article