Some aspects of the embeddings of chain geometries (Q2266443)

Taking up an idea of Hubaut \textit{M. Werner} [Math. Z. 181, 49-54 (1982; Zbl 0477.51005)] showed how to get projective models of n-dimensional chain geometries over algebras. He gave an embedding of the set of points into a grassmannian such that the chains are n-normal curves. There are other known embeddings of chain geometries into projective spaces, for example quadric models of Benz planes [the author: J. Geom. 5, 85-94 (1974; Zbl 0283.50020)] and projective models of Möbius geometries [\textit{M. Werner}: J. Geom. 20, 146-150 (1983; Zbl 0513.51005)]. The aim of the paper is to connect these embeddings. It is shown that there are projections which map the grassmannian models onto the respective other models. By a generalization of the stereographic projection one gets a mapping from the grassmannian onto the belonging algebra.