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Domesticity in projective spaces

Beukje Temmermans, Koen Thas, Hendrik van Maldeghem
2011 Innovations in Incidence Geometry Algebraic Topological and Combinatorial  
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
more » ... collineations of projective spaces for all possible J.
doi:10.2140/iig.2011.12.141 fatcat:4f66ugyzvncfdcpnou3qzhjl7i