Abstract
A geometric hyperplane of a point--line geometry is a proper subspace which meets each line non-trivially. If H is a hyperplane of a projective space P, and the point line geometry Γ has an embedding in P , then the pullback from H is a geometric hyperplane of Γ. We show that all geometric hyperplanes arise in this way for polar spaces of typeD n , the Grassmann space of lines, and the exceptional geometry E 1,6 . The actual geometric hyperplanes are studied in several cases.
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