Characterizations of symplectic polar spaces
Abstract
A polar space S is said to be symplectic if it admits an embedding e in a projective geometry PG(V) such that the eimage e(S) of S 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 (precisely) when S is defined over a field of characteristic 2.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 DOI:
 10.48550/arXiv.2205.14426
 arXiv:
 arXiv:2205.14426
 Bibcode:
 2022arXiv220514426C
 Keywords:

 Mathematics  Symplectic Geometry;
 51A50;
 51b25;
 51e24
 EPrint:
 20 pages/extensively revised