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On a class of hyperplanes of the symplectic and Hermitian dual polar spaces.

Bart De Bruyn UGent (2009) Electronic Journal of Combinatorics. 16(1). p.1-20
abstract
Let $\Delta$ be a symplectic dual polar space (2n-1,K)$ or a Hermitian dual polar space (2n-1,K,\theta)$, \geq 2$. We define a class of hyperplanes of $\Delta$ arising from its Grassmann-embedding and discuss several properties of these hyperplanes. The construction of these hyperplanes allows us to prove that there exists an ovoid of the Hermitian dual polar space (2n-1,K,\theta)$ arising from its Grassmann-embedding if and only if there exists an empty $\theta variety in $\PG(n-1,K)$. Using this result we are able to give the first examples of ovoids in thick dual polar spaces of rank at least 3 which arise from some projective embedding. These are also the first examples of ovoids in thick dual polar spaces of rank at least 3 for which the construction does not make use of transfinite recursion.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
symplectic/Hermitian dual polar space, ovoid, Grassmann embedding
journal title
Electronic Journal of Combinatorics
Electron. J. Combin.
volume
16
issue
1
pages
1 - 20
Web of Science type
Article
Web of Science id
000262254700001
JCR category
MATHEMATICS
JCR impact factor
0.605 (2009)
JCR rank
138/251 (2009)
JCR quartile
3 (2009)
ISSN
1077-8926
language
English
UGent publication?
yes
classification
A1
copyright statement
I don't know the status of the copyright for this publication
id
879105
handle
http://hdl.handle.net/1854/LU-879105
date created
2010-02-24 14:12:53
date last changed
2010-03-05 09:09:52
@article{879105,
  abstract     = {Let \${\textbackslash}Delta\$ be a symplectic dual polar space (2n-1,K)\$ or a Hermitian dual polar space (2n-1,K,{\textbackslash}theta)\$,  {\textbackslash}geq 2\$. We define a class of hyperplanes of \${\textbackslash}Delta\$ arising from its Grassmann-embedding and discuss several properties of these hyperplanes. The construction of these hyperplanes allows us to prove that there exists an ovoid of the Hermitian dual polar space (2n-1,K,{\textbackslash}theta)\$ arising from its Grassmann-embedding if and only if there exists an empty \${\textbackslash}theta variety in \${\textbackslash}PG(n-1,K)\$. Using this result we are able to give the first examples of ovoids in thick dual polar spaces of rank at least 3 which arise from some projective embedding. These are also the first examples of ovoids in thick dual polar spaces of rank at least 3 for which the construction does not make use of transfinite recursion.},
  author       = {De Bruyn, Bart},
  issn         = {1077-8926},
  journal      = {Electronic Journal of Combinatorics},
  keyword      = {symplectic/Hermitian dual polar space,ovoid,Grassmann embedding},
  language     = {eng},
  number       = {1},
  pages        = {1--20},
  title        = {On a class of hyperplanes of the symplectic and Hermitian dual polar spaces.},
  volume       = {16},
  year         = {2009},
}

Chicago
De Bruyn, Bart. 2009. “On a Class of Hyperplanes of the Symplectic and Hermitian Dual Polar Spaces.” Electronic Journal of Combinatorics 16 (1): 1–20.
APA
De Bruyn, B. (2009). On a class of hyperplanes of the symplectic and Hermitian dual polar spaces. Electronic Journal of Combinatorics, 16(1), 1–20.
Vancouver
1.
De Bruyn B. On a class of hyperplanes of the symplectic and Hermitian dual polar spaces. Electronic Journal of Combinatorics. 2009;16(1):1–20.
MLA
De Bruyn, Bart. “On a Class of Hyperplanes of the Symplectic and Hermitian Dual Polar Spaces.” Electronic Journal of Combinatorics 16.1 (2009): 1–20. Print.