%0 Journal Article
%T Imbrex geometries
%A Jeroen Schillewaert
%A Hendrik Van Maldeghem
%J Mathematics
%D 2013
%I arXiv
%X 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 $\mathcal{E}_{6,1}$ by means of a local condition on tangent spaces.
%U http://arxiv.org/abs/1309.3304v1