Ovoids of PG(3,16) are elliptic quadrics
type: Item
instance of: scholarly article
title: Ovoids of PG(3,16) are elliptic quadrics
zbMATH Open document ID: 0707.51014
DOI: 10.1007/BF01222898
author: Christine M. O'Keefe
author: Tim Penttila
published in: Journal of Geometry
publication date: 1990-01-01T00:00:00Z
review text: The authors prove that elliptic quadrics are the only ovoids in projective 3-space PG(3,16) over GF(16). Uniqueness of the inversive plane of order 16 is one of the consequences of this result. The proof is based on a result of \textit{D. G. Glynn} and the second author [A plane representation of ovoids, to appear] which expresses the existence of an ovoid in PG(3,1) in terms of a set of q ovals in PG(2,q). The ovals in PG(2,16) have been determined by \textit{M. Hall} jun. [Ann. Mat. Pura Appl., IV. Ser. 102, 159-176 (1975; Zbl 0313.50013)], cp. also the authors [Eur. J. Comb. 12, 51-60 (1991)], and the authors exclude all ovals which are not conics (with a little help from a small computer).
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 4161556
zbMATH Keywords: elliptic quadric
MaRDI profile type: Publication
cites work: Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe
cites work: Q3796299
cites work: Q3847896
cites work: Q4937820
cites work: Ovals in the Desarguesian plane of order 16
cites work: Q3851217
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cites work: Ovoids and Translation Ovals
cites work: Ovoidal translation planes
full work available at URL: https://doi.org/10.1007/bf01222898
OpenAlex ID: W4248426619
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description: scientific article; zbMATH DE number 4161556