Innovations in Incidence Geometry

Domesticity in projective spaces

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

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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 .

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323072

Digital Object Identifier
doi:10.2140/iig.2011.12.141

Mathematical Reviews number (MathSciNet)
MR2942721

Zentralblatt MATH identifier
1305.51004

Subjects
Primary: 51A10: Homomorphism, automorphism and dualities

Keywords
symplectic polarity displacement projective spaces

Citation

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. https://projecteuclid.org/euclid.iig/1551323072


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References

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