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Generalized Veronesean embeddings of projective spaces, part II: the lax case

(2012) ARS COMBINATORIA. 103. p.65-80
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Abstract
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.

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

MLA
Akça, Z et al. “Generalized Veronesean Embeddings of Projective Spaces, Part II: The Lax Case.” ARS COMBINATORIA 103 (2012): 65–80. Print.
APA
Akça, Z., Bayar, A., Ekmekçi, S., Kaya, R., Thas, J., & Van Maldeghem, H. (2012). Generalized Veronesean embeddings of projective spaces, part II: the lax case. ARS COMBINATORIA, 103, 65–80.
Chicago author-date
Akça, Z, A Bayar, S Ekmekçi, R Kaya, Joseph Thas, and Hendrik Van Maldeghem. 2012. “Generalized Veronesean Embeddings of Projective Spaces, Part II: The Lax Case.” Ars Combinatoria 103: 65–80.
Chicago author-date (all authors)
Akça, Z, A Bayar, S Ekmekçi, R Kaya, Joseph Thas, and Hendrik Van Maldeghem. 2012. “Generalized Veronesean Embeddings of Projective Spaces, Part II: The Lax Case.” Ars Combinatoria 103: 65–80.
Vancouver
1.
Akça Z, Bayar A, Ekmekçi S, Kaya R, Thas J, Van Maldeghem H. Generalized Veronesean embeddings of projective spaces, part II: the lax case. ARS COMBINATORIA. 2012;103:65–80.
IEEE
[1]
Z. Akça, A. Bayar, S. Ekmekçi, R. Kaya, J. Thas, and H. Van Maldeghem, “Generalized Veronesean embeddings of projective spaces, part II: the lax case,” ARS COMBINATORIA, vol. 103, pp. 65–80, 2012.
@article{2522786,
  abstract     = {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.},
  author       = {Akça, Z and Bayar, A and Ekmekçi, S and Kaya, R and Thas, Joseph and Van Maldeghem, Hendrik},
  issn         = {0381-7032},
  journal      = {ARS COMBINATORIA},
  language     = {eng},
  pages        = {65--80},
  title        = {Generalized Veronesean embeddings of projective spaces, part II: the lax case},
  volume       = {103},
  year         = {2012},
}

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