{"title":"The feet of orthogonal Buekenhout–Metz unitals","authors":"S.G. Barwick, W.-A. Jackson, P. Wild","doi":"10.1515/advgeom-2024-0001","DOIUrl":null,"url":null,"abstract":"In this article we look at the geometric structure of the feet of an orthogonal Buekenhout–Metz unital 𝓤 in PG(2, <jats:italic>q</jats:italic> <jats:sup>2</jats:sup>). We show that the feet of each point form a set of type (0, 1, 2, 4). Further, we discuss the structure of any 4-secants, and determine exactly when the feet form an arc.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":"286 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/advgeom-2024-0001","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this article we look at the geometric structure of the feet of an orthogonal Buekenhout–Metz unital 𝓤 in PG(2, q2). We show that the feet of each point form a set of type (0, 1, 2, 4). Further, we discuss the structure of any 4-secants, and determine exactly when the feet form an arc.
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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