On transparent embeddings of point-line geometries

Abstract

We introduce the class of transparent embeddings for a point-line geometry $\Gamma =(\mathcal{P},\mathcal{L})$ as the class of full projective embeddings $\epsilon$ of $\Gamma$ such that the preimage of any projective line fully contained in $\epsilon (\mathcal{P})$ is a line of $\Gamma$. We will then investigate the transparency of Plücker 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.

28 Pages/revised version after review

References in corpus (1)

• On spinor varieties and their secants

Cited by in corpus (4)

• Line Hermitian Grassmann Codes and their Parameters
• Grassmann embeddings of polar Grassmannians
• Grassmannians of codes
• Maps related to polar spaces preserving a Weyl distance or an incidence condition