Let Γ be an embeddable non-degenerate polar space of finite rank n≥2. Assuming that Γ admits the universal embedding (which is true for all embeddable polar spaces except grids of order at least 5 and certain generalized quadrangles defined over quaternion division rings), let ε:Γ→PG(V) be the universal embedding of Γ. Let S be a subspace of Γ and suppose that S, regarded as a polar space, has non-degenerate rank at least 2. We shall prove that S is the ε-preimage of a projective subspace of PG(V).

Cardinali, I., Giuzzi, L., Pasini, A. (2021). Nearly all subspaces of a classical polar space arise from its universal embedding. LINEAR ALGEBRA AND ITS APPLICATIONS, 627, 287-307 [10.1016/j.laa.2021.06.013].

Nearly all subspaces of a classical polar space arise from its universal embedding

Cardinali I.
;
2021

Abstract

Let Γ be an embeddable non-degenerate polar space of finite rank n≥2. Assuming that Γ admits the universal embedding (which is true for all embeddable polar spaces except grids of order at least 5 and certain generalized quadrangles defined over quaternion division rings), let ε:Γ→PG(V) be the universal embedding of Γ. Let S be a subspace of Γ and suppose that S, regarded as a polar space, has non-degenerate rank at least 2. We shall prove that S is the ε-preimage of a projective subspace of PG(V).
Cardinali, I., Giuzzi, L., Pasini, A. (2021). Nearly all subspaces of a classical polar space arise from its universal embedding. LINEAR ALGEBRA AND ITS APPLICATIONS, 627, 287-307 [10.1016/j.laa.2021.06.013].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1178651