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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 17, Issue 4

Issues

The exterior splash in PG(6, q): carrier conics

Susan G. Barwick / Wen-Ai Jackson
Published Online: 2017-10-16 | DOI: https://doi.org/10.1515/advgeom-2017-0032

Abstract

Let π be a subplane of PG(2,q3) of order q that is exterior to . The exterior splash of π is the set of q2+q+1 points on that lie on the extended lines of π. Exterior splashes are projectively equivalent to scattered linear sets of rank 3, covers of the circle geometry CG(3,q), and hyper-reguli of PG(5,q). In this article we use the Bruck–Bose representation in PG(6,q) to give a geometric characterisation of carrier conics of π in terms of the covers of the exterior splash of π. We also investigate properties of subplanes of order q with a common exterior splash, and study the intersection of two exterior splashes.

Keywords: Bruck–Bose representation; subplanes; exterior splash; conics

MSC 2010: 51E20

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About the article


Received: 2015-11-06

Published Online: 2017-10-16

Published in Print: 2017-10-26


Citation Information: Advances in Geometry, Volume 17, Issue 4, Pages 407–422, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0032.

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