Generalized Veronesean embeddings of projective spaces, part II: the lax case
 Author
 Z Akça, A Bayar, S Ekmekçi, R Kaya, Joseph Thas (UGent) and Hendrik Van Maldeghem (UGent)
 Organization
 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 subVeroneseans (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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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU2522786
 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 authordate
 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 authordate (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 subVeroneseans (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 = {03817032}, journal = {ARS COMBINATORIA}, language = {eng}, pages = {6580}, title = {Generalized Veronesean embeddings of projective spaces, part II: the lax case}, volume = {103}, year = {2012}, }