Generalized Veronesean embeddings of projective spaces


We classify all embeddings θ: PG(n, q) → PG(d, q), with \(d \geqslant \tfrac{{n(n + 3)}} {2}\), such that θ maps the set of points of each line to a set of coplanar points and such that the image of θ generates PG(d, q). It turns out that d = ½n(n+3) and all examples are related to the quadric Veronesean of PG(n, q) in PG(d, q) and its projections from subspaces of PG(d, q) generated by sub-Veroneseans (the point sets corresponding to subspaces of PG(n, q)). With an additional condition we generalize this result to the infinite case as well.

This is a preview of subscription content, access via your institution.


  1. [1]

    J. W. P. Hirschfeld and J. A. Thas: General Galois Geometries, Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1991.

    MATH  Google Scholar 

  2. [2]

    J. Schillewaert and H. Van Maldeghem: Quadric Veronesean caps, Discrete Math., submitted.

  3. [3]

    J. A. Thas and H. Van Maldeghem: Characterizations of the finite quadric Veroneseans \(\mathcal{V}_n^{2^n }\), Quart. J. Math. 55 (2004), 99–113.

    Article  MATH  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Joseph A. Thas.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Thas, J.A., Van Maldeghem, H. Generalized Veronesean embeddings of projective spaces. Combinatorica 31, 615–629 (2011).

Download citation

Mathematics Subject Classification (2000)

  • 51E20