2013/09/12 by Jeroen Schillewaert, Hendrik Van Maldeghem, Schillewaert, Jeroen +1
Mathematics · #51 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Representation Theory (math.RT) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1309.3304
openalex publication_date 2013/09/12 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We introduce an axiom on strong parapolar spaces of diameter 2, which arises naturally in the framework of Hjelmslev geometries. This way, we characterize the Hjelmslev-Moufang plane and its relatives (line Grassmannians, certain half-spin geometries and Segre geometries). At the same time we provide a more general framework for a Lemma of Cohen, which is widely used to study parapolar spaces. As an application, if the geometries are embedded in projective space, we provide a common characterization of (projections of) Segre varieties, line Grassmann varieties, half-spin varieties of low rank, and the exceptional variety E6,1 by means of a local condition on tangent spaces.