This article classifies regular polarities of exceptional geometries of type E6, revealing new subgeometries.
A polarity of an exceptional geometry of type E6 is called regular if its fix structure, viewed as simplicial complex, is a building. Polarities which do not act trivial on the underlying field were classified a long time ago by Jacques Tits. In the present paper, we classify the regular polarities of exceptional geometries of type E6 that act trivial on the underlying (arbitrary) field. As a result, we discover new subgeometries of the exceptional geometry of type E6.
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Maldeghem et al. (2025) studied this question.
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