Vol. 12, No. 1, 2011

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Domesticity in projective spaces

Beukje Temmermans, Koen Thas and Hendrik J. van Maldeghem

Vol. 12 (2011), No. 1, 141–149
Abstract

Let J be a set of types of subspaces of a projective space. Then a collineation or a duality is called J-domestic if it maps no flag of type J to an opposite one. In this paper, we characterize symplectic polarities as the only dualities of projective spaces that map no chamber to an opposite one. This implies a complete characterization of all J-domestic dualities of an arbitrary projective space for all type subsets J. We also completely characterize and classify J-domestic collineations of projective spaces for all possible J.

Keywords
symplectic polarity, displacement, projective spaces
Mathematical Subject Classification 2010
Primary: 51A10
Milestones
Received: 10 September 2010
Accepted: 2 March 2011
Authors
Beukje Temmermans
Koen Thas
Department of Mathematics
Ghent University
Krijgslaan 281
S25
9000 Ghent
Belgium
Hendrik J. van Maldeghem
Vakgroep Zuivere Wiskunde en Computeralgebra
University of Ghent
9000 Gent
Belgium