Abstract. The Grassmann space of fc-subspaces of a polar space is defined and its geometry is examined. In particular, its cliques, subspaces and automorphisms are characterized. An analogue of Chow's theorem for the Grassmann space of fc-subspaces of a polar spaces is proved.

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Two geometries can be considered in the structure of linear complements: an affine spine space and an affine space. An affine spine space arises from a space of pencils. In terms of this geometry an affine partial line space may be defined. It is extensible to the affine space. Automorphisms of the affine spine space are automorphisms of appropriate affine space. (2000): 51A15, 51A45. Mathematics Subject Classification