On transparent embeddings of point-line geometries

摘要

We introduce the class of transparent embeddings for a point line geometry Gamma = (P, L) as the class of full projective embeddings epsilon of Gamma such that the preimage of any projective line fully contained in epsilon(P) is a line of Gamma. We will then investigate the transparency of Plucker embeddings of projective and polar grassmannians and spin embeddings of half-spin geometries and dual polar spaces of orthogonal type. As an application of our results on transparency, we will derive several Chow-like theorems for polar grassmannians and half-spin geometries. (C) 2017 Elsevier Inc. All rights reserved.