Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/17776
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Type: Journal article
Title: Eggs in PG(4n - 1,q)q even, containing a pseudo-pointed conic
Author: Brown, M.
Lavrauw, M.
Citation: European Journal of Combinatorics, 2005; 26(1):117-128
Publisher: Academic Press Ltd Elsevier Science Ltd
Issue Date: 2005
ISSN: 0195-6698
Statement of
Responsibility: 
Matthew R. Brown, Michel Lavrauw
Abstract: An ovoid of PG(3,q) can be defined as a set of q2+1 points with the property that every three points span a plane and at every point there is a unique tangent plane. In 2000 M.R. Brown (J. Geom. 67 (2000) 61) proved that if an ovoid of PG(3,q), q even, contains a pointed conic, then either q=4 and the ovoid is an elliptic quadric, or q=8 and the ovoid is a Tits ovoid. Generalising the definition of an ovoid to a set of (n-1)-spaces of PG(4n-1,q), J.A. Thas (Rend. Mat. (6) 4 (1971) 459) introduced the notion of pseudo-ovoids or eggs: a set of q2n+1(n-1)-spaces in PG(4n-1,q), with the property that any three egg elements span a (3n-1)-space and at every egg element there is a unique tangent (3n-1)-space. We prove that an egg in PG(4n-1,q), q even, contains a pseudo-pointed conic, that is, a pseudo-oval arising from a pointed conic of PG(2,qn), q even, if and only if the egg is elementary and the ovoid is either an elliptic quadric in PG(3,4) or a Tits ovoid in PG(3,8). © 2004 Elsevier Ltd. All rights reserved.
DOI: 10.1016/j.ejc.2003.12.014
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Pure Mathematics publications

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