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Generalized Veronesean embeddings of projective spaces

Joseph Thas (UGent) and Hendrik Van Maldeghem (UGent)
(2011) COMBINATORICA. 31(5). p.615-629
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Abstract
We classify all embeddings theta: PG(n, q) -> PG(d, q), with d >= n(n+3)/2 such that theta maps the set of points of each line to a set of coplanar points and such that the image of theta generates PG(d, q). It turns out that d = 1/2n(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.

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Please use this url to cite or link to this publication:

MLA
Thas, Joseph, and Hendrik Van Maldeghem. “Generalized Veronesean Embeddings of Projective Spaces.” COMBINATORICA 31.5 (2011): 615–629. Print.
APA
Thas, J., & Van Maldeghem, H. (2011). Generalized Veronesean embeddings of projective spaces. COMBINATORICA, 31(5), 615–629.
Chicago author-date
Thas, Joseph, and Hendrik Van Maldeghem. 2011. “Generalized Veronesean Embeddings of Projective Spaces.” Combinatorica 31 (5): 615–629.
Chicago author-date (all authors)
Thas, Joseph, and Hendrik Van Maldeghem. 2011. “Generalized Veronesean Embeddings of Projective Spaces.” Combinatorica 31 (5): 615–629.
Vancouver
1.
Thas J, Van Maldeghem H. Generalized Veronesean embeddings of projective spaces. COMBINATORICA. 2011;31(5):615–29.
IEEE
[1]
J. Thas and H. Van Maldeghem, “Generalized Veronesean embeddings of projective spaces,” COMBINATORICA, vol. 31, no. 5, pp. 615–629, 2011.
@article{2458020,
  abstract     = {We classify all embeddings theta: PG(n, q) -> PG(d, q), with d >= n(n+3)/2 such that theta maps the set of points of each line to a set of coplanar points and such that the image of theta generates PG(d, q). It turns out that d = 1/2n(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.},
  author       = {Thas, Joseph and Van Maldeghem, Hendrik},
  issn         = {0209-9683},
  journal      = {COMBINATORICA},
  language     = {eng},
  number       = {5},
  pages        = {615--629},
  title        = {Generalized Veronesean embeddings of projective spaces},
  url          = {http://dx.doi.org/10.1007/s00493-011-2651-2},
  volume       = {31},
  year         = {2011},
}

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