Splitness of the Veronesean and the Taniguchi dual hyperovals
type: Item
instance of: scholarly article
title: Splitness of the Veronesean and the Taniguchi dual hyperovals
zbMATH Open document ID: 1475.51008
published in: Discrete Mathematics
publication date: 2019-01-22T00:00:00Z
review text: Let \(V\) be an \((n+m)\)-dimensional vector space over the finite field \(\mathbb{F}_q\). A set \(\mathcal{H}\) of \(\frac{q^n-1}{q-1}+1\) \(n\)-dimensional subspaces (\(n \ge 3\)) of \(V\) is called a dual hyperoval of \(V\) (DHO in short) if \(\langle \mathcal{H} \rangle = V\), \(\dim(X \cap Y) = 1\) and \(X \cap Y \cap Z = {0}\) for any three distinct members \(X , Y , Z \in\mathcal{H}\). A DHO \(\mathcal{H}\) is said to be of split type if there exists a subspace \(Y\) of \(V\) such that \(Y \oplus X = V\) for all \(X \in\mathcal{H}\). In the nice paper under review, the case \(m = n(n-1)/2\) and \(q = 2\) is investigated. There are four known DHOs, called the Huybrechts, Buratti-Del Fra, Veronesean and Taniguchi DHO. It is known that the first two DHOs are of split type. Here, the author shows that the Veronesean and Taniguchi DHOs also are of split type.
reviewed by: Francesco Pavese
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 51A45
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 7004813
zbMATH Keywords: dimensional dual hyperoval (DHO)
zbMATH Keywords: split DHO
zbMATH Keywords: Veronesean DHO
zbMATH Keywords: Taniguchi DHO
author: Satoshi Yoshiara
MaRDI profile type: Publication
full work available at URL: j.disc.2018.11.019
OpenAlex ID: W2904966799
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Wikidata QID: Q128787946
DOI: 10.1016/J.DISC.2018.11.019
description: scientific article; zbMATH DE number 7004813