Generalized Veronesean embeddings of projective spaces
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AbstractWe 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.
[1] J. Thas,et al. General Galois geometries , 1992 .
[2] Hendrik Van Maldeghem,et al. Characterizations of the finite quadric Veroneseans V-n(2n) , 2004 .