{"title":"Characterizations of symplectic polar spaces","authors":"I. Cardinali, H. Cuypers, L. Giuzzi, A. Pasini","doi":"10.1515/advgeom-2023-0006","DOIUrl":null,"url":null,"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.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2022-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/advgeom-2023-0006","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
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.
期刊介绍：
Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.
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