Generalized Veronesean embeddings of projective spaces Part II The lax case

Akça Z., Bayar A., Ekmekçi S., Kaya R., Thas J. A., Van Maldeghem H.

Ars Combinatoria, vol.3, no.0, pp.65-80, 2012 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 3 Issue: 0
  • Publication Date: 2012
  • Journal Name: Ars Combinatoria
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.65-80
  • Eskisehir Osmangazi University Affiliated: Yes


We classify all embeddings theta : PG(n,K) > PG(d, F), with d >= n(n+3)/2 and K, F skew fields with vertical bar K vertical bar > 2, such that 0 maps the set of points of each line of PG(n,K) to a set of coplanar points of PG(d, F), and such that the image of theta generates PG(d, F). It turns out that d = 1/2n(n + 3) and all examples "essentially" arise from a similar "full" embedding theta' : PG(n, K) -> PG(d,K) by identifying K with subfields of IF and embedding PG(d, K) into PG(d, F) by several ordinary field extensions. These "full" embeddings satisfy one more property and are classified in [5]. They relate to the quadric Veronesean of PG(n, K) in PG(d, K) and its projections from subspaces of PG(d, K) generated by sub-Veroneseans (the point sets corresponding to subspaces of PG(n,K)), if K is commutative, and to a degenerate analogue of this, if K is noncommutative.