Characterizations of symplectic polar spaces-Reference-Cited by-同舟云学术

Characterizations of symplectic polar spaces

Published:2023-05-01 Issue:2 Volume:23 Page:281-292
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Cardinali Ilaria¹,Cuypers Hans²,Giuzzi Luca³,Pasini Antonio¹

Affiliation:

1. Dep. Information Engineering and Mathematics, University of Siena , Via Roma 56, 53100 Siena , Italy

2. Dep. Mathematics and Computer Sciences, Eindhoven University of Technology , 5600 MB Eindhoven , Netherlands

3. D.I.C.A.T.A.M., University of Brescia , Via Branze 43, 25123 Brescia , Italy

Abstract

Abstract A polar space 𝒮 is called symplectic if it admits a projective embedding ε : 𝒮 → PG(V) such that the image ε(𝒮) of 𝒮 by ε is defined by an alternating form of V. In this paper we characterize symplectic polar spaces in terms of their incidence properties, with no mention of peculiar properties of their embeddings. This is relevant especially when 𝒮 admits different (non-isomorphic) embeddings, as it is the case when 𝒮 is defined over a field of characteristic 2.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2023-0006/pdf

Reference23 articles.

1. F. Buekenhout, A. M. Cohen, Diagram geometry. Springer 2013. MR3014979 Zbl 1284.51001

2. P. J. Cameron, Ovoids in infinite incidence structures. Arch. Math. Basel) 62 (1994), 189–192. MR1255643 Zbl 0816.51005

3. I. Cardinali, L. Giuzzi, A. Pasini, Nearly all subspaces of a classical polar space arise from its universal embedding. Linear Algebra Appl. 627 (2021), 287–307. MR4283256 Zbl 1469.51001

4. A. M. Cohen, E. E. Shult, Affine polar spaces. Geom. Dedicata35 (1990), 43–76. MR1066558 Zbl 0755.51004

5. H. Cuypers, P. Johnson, A. Pasini, On the embeddability of polar spaces. Geom. Dedicata44 (1992), 349–358. MR1193124 Zbl 0772.51007

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