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 $J$.

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Mathematical Subject Classification 2010

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