## Innovations in Incidence Geometry

### Domesticity in projective spaces

#### 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
Accepted: 2 March 2011
First available in Project Euclid: 28 February 2019

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

#### 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

#### References

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