On absolutely universal embeddings

Authors:
R. J. Blok;A. Pasini
Affiliations:
Department of Mathematics, Michigan State University, East Lansing MI;Department of Mathematics, University of Siena, Via del Capitano 15, I-53100 Siena, Italy
Venue:
Discrete Mathematics - Special issue: Combinatorics 2000
Year:
2003

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Abstract

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.