On existence of embeddings for point-line geometries

Abstract

We describe a construction of a point-line presheaf on a point-line geometry from a set of presheaves on subspaces of the geometry. Then we combine our construction with theorems of M. Ronan to give a new proof of the fact that all polar spaces of finite rank at least four, and several other Grassmann geometries of spherical buildings, are embeddable in projective spaces.