We introduce the class of transparent embeddings for a point-line geometry Γ=(P,L) as the class of full projective embeddings ε of Γ such that the preimage of any projective line fully contained in ε(P) is a line of Γ. 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.
Titolo: | On transparent embeddings of point-line geometries |
Autori: | |
Data di pubblicazione: | 2018 |
Rivista: | |
Abstract: | We introduce the class of transparent embeddings for a point-line geometry Γ=(P,L) as the class of full projective embeddings ε of Γ such that the preimage of any projective line fully contained in ε(P) is a line of Γ. 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. |
Handle: | http://hdl.handle.net/11379/498035 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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