Imbrex geometries
Metric Geometry
2013-09-16 v1 Combinatorics
Representation Theory
Abstract
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 by means of a local condition on tangent spaces.
Cite
@article{arxiv.1309.3304,
title = {Imbrex geometries},
author = {Jeroen Schillewaert and Hendrik Van Maldeghem},
journal= {arXiv preprint arXiv:1309.3304},
year = {2013}
}