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arXiv · 2205.14426

Characterizations of symplectic polar spaces

Ilaria Cardinali·Hans Cuypers·Luca Giuzzi·Antonio Pasini
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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 e-image 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.

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Ilaria Cardinali, Hans Cuypers, Luca Giuzzi, Antonio Pasini. 2022-05-28. Characterizations of symplectic polar spaces. https://doi.org/10.1515/advgeom-2023-0006

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