Uniqueness of the inversive plane of order sixty-four
type: Item
instance of: scholarly article
title: Uniqueness of the inversive plane of order sixty-four
zbMATH Open document ID: 1487.51005
author: Tim Penttila
published in: Designs, Codes and Cryptography
publication date: 2022-03-21T00:00:00Z
review text: In this paper, the author classifies ovoids in \(\mathrm{PG}(3,64)\) as elliptic quadrics. The author starts with a nice historical overview of some main results leading up to this classification. The computer techniques used are similar as in the paper of \textit{C. M. O'Keefe} et al. [J. Geom. 50, No. 1--2, 143--150 (1994; Zbl 0805.51004)] which dealt with the classification of ovoids in \(\mathrm{PG}(3,32)\). There are several corollaries for related concepts in finite geometry. Most notably, it follows that there is a unique inversive plane of order 64. Further consequences for generalised quadrangles and translation planes are described in the last section.
reviewed by: Geertrui Van de Voorde
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 7494016
zbMATH Keywords: inversive planes
zbMATH Keywords: ovoids
zbMATH Keywords: ovals
MaRDI profile type: Publication
full work available at URL: s10623-022-01014-6
OpenAlex ID: W4210931514
Wikidata QID: Q114849784
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DOI: 10.1007/S10623-022-01014-6
description: scientific article; zbMATH DE number 7494016