Canonical Linearization of Pure Geometries

Abstract In this article a construction is given which canonically associates pure geometries in linear diagrams to arbitrary pure geometries. Also given are reverse constructions in some special cases. This partially answers a question in Buekenhout (“Proceedings of the Conference in Honour of H. Lenz” (Sect. 9.16, Comments), Lecture Notes in Mathematics, No. 893, Springer-Verlag, New York/Berlin, 1981).