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

(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:
http://hdl.handle.net/1854/LU-879105

- author
- Bart De Bruyn UGent
- organization
- year
- 2009
- 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.