Generalized Veronesean embeddings of projective spaces

@article{Thas2011GeneralizedVE,
  title={Generalized Veronesean embeddings of projective spaces},
  author={Joseph A. Thas and Hendrik Van Maldeghem},
  journal={Combinatorica},
  year={2011},
  volume={31},
  pages={615-629}
}
We classify all embeddings θ : PG(n, q) −→ PG(d, q), with d ≥ 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 = 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… CONTINUE READING

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