On absolutely universal embeddings Original Research Article

It is well known that, given a point-line geometry Γ and a projective embedding ε : Γ→PG(V), if dim(V) equals the size of a generating set of Γ, then ε is not derived from any other embedding. Thus, if Γ admits an absolutely universal embedding, then ε is absolutely universal. In this paper, without assuming the existence of any absolutely universal embedding, we give sufficient conditions for an embedding ε as above to be absolutely universal.