Ovals in translation hyperovals and ovoids
type: Item
instance of: scholarly article
title: Ovals in translation hyperovals and ovoids
zbMATH Open document ID: 0885.51010
author: Christine M. O'Keefe
author: Tim Penttila
published in: European Journal of Combinatorics
publication date: 1998-04-20T00:00:00Z
review text: An ovoid in \(\text{PG}(3,q)\) is a set of \(q^2+ 1\) points, no three of which are collinear. A hyperoval in \(\text{PG}(2, q)\) is a set of \(q+2\) points, no three of which are collinear. (A hyperoval cannot exist unless \(q\) is even.) A hyperoval is a translation oval if it is fixed by a group of order \(q\) consisting of elations, all with the same axis. The main result is that if \(O\) is an ovoid of \(\text{PG}(3, q)\), \(q\) even such that every secant plane section is an oval contained in a hyperoval, then \(O\) is either an elliptic quadric or a Tits ovoid.
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 1066021
zbMATH Keywords: translation hyperovals
zbMATH Keywords: ovoid
zbMATH Keywords: oval
reviewed by: Theodore G. Ostrom
MaRDI profile type: Publication
full work available at URL: eujc.1996.0127
OpenAlex ID: W2033703688
DOI: 10.1006/EUJC.1996.0127
description: scientific article; zbMATH DE number 1066021