On \(d\)-dimensional dual hyperovals
type: Item
instance of: scholarly article
title: On \(d\)-dimensional dual hyperovals
zbMATH Open document ID: 0948.51008
DOI: 10.1023/A:1005244404475
published in: Geometriae Dedicata
publication date: 2000-07-06T00:00:00Z
review text: Let \(\Pi=\text{PG}(n,q)\) be the \(n\)-dimensional projective space over the finite field with \(q\) elements. A \(d\)-dimensional dual hyperoval is a family \(F\) of \(d\)-dimensional subspaces of \(\Pi\) such that each point of \(\Pi\) is contained in 0 or 2 elements of \(F\), any two elements of \(F\) intersect in exactly one point, and the set of points belonging to the elements of \(F\) spans \(\Pi\). A \(d\)-dimensional dual hyperoval is said to satisfy property (T), if for all \(U,V,W\in F\), we have \(\dim(\langle U,V\rangle\cap W)=1\). It is said to be \textit{2-transitive}, if its stabilizer in \(\Aut(\Pi)\) acts 2-transitively on \(F\). After giving some examples, parameters and restrictions for \(d\)-dimensional dual hyperovals, the author gives a complete classification of 2-dimensional dual hyperovals in \(\text{PG}(4,2)\) and in \(\text{PG}(5,2)\). This yields a complete classification of 2-dimensional dual hyperovals satisfying property (T) as well as a classification of 2-transitive 2-dimensional dual hyperovals.
reviewed by: J. Eisfeld
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51E24
zbMATH DE Number: 1436010
zbMATH Keywords: dual hyperoval
zbMATH Keywords: classification
author: Alberto Del Fra
MaRDI profile type: Publication
full work available at URL: a:1005244404475
OpenAlex ID: W1515697227
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description: scientific article; zbMATH DE number 1436010