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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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1615-7168
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Volume 11, Issue 2

Issues

Polarities of Schellhammer planes

Steffen Poppitz / Markus Stroppel
Published Online: 2011-04-08 | DOI: https://doi.org/10.1515/advgeom.2010.048

Abstract

We construct polarities for projective planes admitting a group of automorphisms that acts regularly on the complements of an anti-flag in the point and line set. In particular, we determine all polarities of the compact connected planes studied by I. Schellhammer and by P. Sperner. For both classes of planes we solve the conjugacy problem, and determine the set of absolute points for each one of the polarities. Among these polarities we find the first examples of elliptic polarities in non-Moufang compact projective planes.

About the article

Received: 2010-08-21

Published Online: 2011-04-08

Published in Print: 2011-04-01


Citation Information: Advances in Geometry, Volume 11, Issue 2, Pages 319–336, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom.2010.048.

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[1]
Rainer Löwen
Advances in Geometry, 2011, Volume 11, Number 2

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