Innovations in Incidence Geometry

Domesticity in projective spaces

Beukje Temmermans, Joseph A. Thas, and Hendrik van Maldeghem

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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 .

Article information

Innov. Incidence Geom., Volume 12, Number 1 (2011), 141-149.

Received: 10 September 2010
Accepted: 2 March 2011
First available in Project Euclid: 28 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 51A10: Homomorphism, automorphism and dualities

symplectic polarity displacement projective spaces


Temmermans, Beukje; Thas, Joseph A.; van Maldeghem, Hendrik. Domesticity in projective spaces. Innov. Incidence Geom. 12 (2011), no. 1, 141--149. doi:10.2140/iig.2011.12.141.

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  • P. Abramenko and K. Brown, Automorphisms of non-spherical buildings have unbounded displacement, Innov. Inc. Geom. 10 (2010), 1–13.
  • B. Leeb, A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry, Bonner Mathematische Schriften [Bonn Mathematical Publications] 326, Universität Bonn, Mathematisches Institut, Bonn, 2000.