We introduce the class of transparent embeddings for a point-line geometry Î=(P,L) as the class of full projective embeddings ε of Î such that the preimage of any projective line fully contained in ε(P) is a line of Î. 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.
Cardinali, I., Giuzzi, L., Pasini, A. (2018). On transparent embeddings of point-line geometries. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 155, 190-224 [10.1016/j.jcta.2017.11.001].
On transparent embeddings of point-line geometries
Cardinali, Ilaria;Pasini, Antonio
2018-01-01
Abstract
We introduce the class of transparent embeddings for a point-line geometry Î=(P,L) as the class of full projective embeddings ε of Î such that the preimage of any projective line fully contained in ε(P) is a line of Î. 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.File | Dimensione | Formato | |
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https://hdl.handle.net/11365/1029549