Adjacency in generalized projective Veronese spaces
type: Item
instance of: scholarly article
title: Adjacency in generalized projective Veronese spaces
zbMATH Open document ID: 1139.51021
DOI: 10.1007/BF02960859
author: I. Golonko
author: M. Prażmowska
author: K. Prażmowski
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2007-08-29T00:00:00Z
review text: 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.
reviewed by: Jonathan Schaer
Mathematics Subject Classification ID: 51M35
Mathematics Subject Classification ID: 51A99
zbMATH DE Number: 5184532
zbMATH Keywords: generalized Veronese spaces (associated with a partial linear space)
zbMATH Keywords: \(\Gamma\)-space
zbMATH Keywords: exchange space
zbMATH Keywords: adjacency
zbMATH Keywords: clique
zbMATH Keywords: strong subspace
zbMATH Keywords: pencils of strong subspaces
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5184532