A geometrical construction of the oval(s) associated with an a-flock
Date
2004
Authors
Brown, M.
Thas, J.
Editors
Brown, M.R.
Thas, J.A.
Thas, J.A.
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
Advances in Geometry, 2004; 4(1):9-17
Statement of Responsibility
Conference Name
Abstract
It is known, via algebraic methods, that a flock of a quadratic cone in PG(3, q) gives rise to a family of q + 1 ovals of PG(2, q) and similarly that a flock of a cone over a translation oval that is not a conic gives rise to an oval of PG(2, q). In this paper we give a geometrical construction of these ovals and provide an elementary geometrical proof of the construction. Further we also give a geometrical construction of a spread of the GQ T <inf>2</inf>(Ο) for Ο an oval corresponding to a flock of a translation oval cone in PG(3, q), previously constructed algebraically. © de Gruyter 2004.