 Author
 Bart De Bruyn (UGent)
 Organization
 Abstract
 Let e: S > Sigma be a full polarized projective embedding of a dense near polygon S, i.e., for every point p of S, the set H(p) of points at nonmaximal distance from p is mapped by e into a hyperplane Pi(p) of Sigma. We show that if every line of S is incident with precisely three points or if S satisfies a certain property (P(de)) then the map p bar right arrow Pi p defines a full polarized embedding e* (the socalled dual embedding of e) of S into a subspace of the dual Sigma* of Sigma. This generalizes a result of [6] where it was shown that every embedding of a thick dual polar space has a dual embedding. We determine which known dense near polygons satisfy property (P(de)). This allows us to conclude that every full polarized embedding of a known dense near polygon has a dual embedding.
 Keywords
 polarized embedding, GEOMETRIES, hyperplane, dual embedding, near polygon
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU3101091
 Chicago
 De Bruyn, Bart. 2012. “Dual Embeddings of Dense Near Polygons.” Ars Combinatoria 103: 33–54.
 APA
 De Bruyn, B. (2012). Dual embeddings of dense near polygons. ARS COMBINATORIA, 103, 33–54.
 Vancouver
 1.De Bruyn B. Dual embeddings of dense near polygons. ARS COMBINATORIA. 2012;103:33–54.
 MLA
 De Bruyn, Bart. “Dual Embeddings of Dense Near Polygons.” ARS COMBINATORIA 103 (2012): 33–54. Print.
@article{3101091, abstract = {Let e: S {\textrangle} Sigma be a full polarized projective embedding of a dense near polygon S, i.e., for every point p of S, the set H(p) of points at nonmaximal distance from p is mapped by e into a hyperplane Pi(p) of Sigma. We show that if every line of S is incident with precisely three points or if S satisfies a certain property (P(de)) then the map p bar right arrow Pi p defines a full polarized embedding e* (the socalled dual embedding of e) of S into a subspace of the dual Sigma* of Sigma. This generalizes a result of [6] where it was shown that every embedding of a thick dual polar space has a dual embedding. We determine which known dense near polygons satisfy property (P(de)). This allows us to conclude that every full polarized embedding of a known dense near polygon has a dual embedding.}, author = {De Bruyn, Bart}, issn = {03817032}, journal = {ARS COMBINATORIA}, language = {eng}, pages = {3354}, title = {Dual embeddings of dense near polygons}, url = {http://cage.ugent.be/geometry/Files/280/dual\_emb.pdf}, volume = {103}, year = {2012}, }