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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 |
Published version: | http://dx.doi.org/10.1016/j.ejc.2003.12.014 |
Appears in Collections: | Aurora harvest 6 Pure Mathematics publications |
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