### Some subspaces of the projective space PG(Lambda(K) V) related to regular spreads of PG(V)

(2010) ELECTRONIC JOURNAL OF LINEAR ALGEBRA. 20. p.354-366- abstract
- Let V be a 2m-dimensional vector space over a field F (m >= 2) and let k is an element of {1, ... , 2m - 1}. Let A(2m-1,k) denote the Grassmannian of the (k - 1)-dimensional subspaces of PG(V) and let e(gr) denote the Grassmann embedding of A(2m-1,k) into PG(Lambda(k) V). Let S be a regular spread of PG(V) and let X-S denote the set of all ( k - 1)-dimensional subspaces of PG(V) which contain at least one line of S. Then we show that there exists a subspace Sigma of PG(Lambda(k) V) for which the following holds: (1) the projective dimension of Sigma is equal to ((2m)(k)) - 2 . ((m)(k)) - 1; (2) a (k - 1)-dimensional subspace alpha of PG(V) belongs to X-S if and only if e(gr)(alpha) is an element of Sigma; (3) Sigma is generated by all points e(gr)(p), where p is some point of X-S.

Please use this url to cite or link to this publication:
http://hdl.handle.net/1854/LU-1105471

- author
- Bart De Bruyn UGent
- organization
- year
- 2010
- type
- journalArticle (original)
- publication status
- published
- subject
- keyword
- Klein correspondence, Grassmann embedding, Regular spread, Grassmannian
- journal title
- ELECTRONIC JOURNAL OF LINEAR ALGEBRA
- Electron. J. Linear Algebra
- volume
- 20
- pages
- 354 - 366
- Web of Science type
- Article
- Web of Science id
- 000281206100002
- JCR category
- MATHEMATICS
- JCR impact factor
- 0.808 (2010)
- JCR rank
- 73/276 (2010)
- JCR quartile
- 2 (2010)
- ISSN
- 1081-3810
- language
- English
- UGent publication?
- yes
- classification
- A1
- copyright statement
*I have transferred the copyright for this publication to the publisher*- id
- 1105471
- handle
- http://hdl.handle.net/1854/LU-1105471
- date created
- 2011-01-20 10:15:06
- date last changed
- 2016-12-19 15:41:28

@article{1105471, abstract = {Let V be a 2m-dimensional vector space over a field F (m {\textrangle}= 2) and let k is an element of \{1, ... , 2m - 1\}. Let A(2m-1,k) denote the Grassmannian of the (k - 1)-dimensional subspaces of PG(V) and let e(gr) denote the Grassmann embedding of A(2m-1,k) into PG(Lambda(k) V). Let S be a regular spread of PG(V) and let X-S denote the set of all ( k - 1)-dimensional subspaces of PG(V) which contain at least one line of S. Then we show that there exists a subspace Sigma of PG(Lambda(k) V) for which the following holds: (1) the projective dimension of Sigma is equal to ((2m)(k)) - 2 . ((m)(k)) - 1; (2) a (k - 1)-dimensional subspace alpha of PG(V) belongs to X-S if and only if e(gr)(alpha) is an element of Sigma; (3) Sigma is generated by all points e(gr)(p), where p is some point of X-S.}, author = {De Bruyn, Bart}, issn = {1081-3810}, journal = {ELECTRONIC JOURNAL OF LINEAR ALGEBRA}, keyword = {Klein correspondence,Grassmann embedding,Regular spread,Grassmannian}, language = {eng}, pages = {354--366}, title = {Some subspaces of the projective space PG(Lambda(K) V) related to regular spreads of PG(V)}, volume = {20}, year = {2010}, }

- Chicago
- De Bruyn, Bart. 2010. “Some Subspaces of the Projective Space PG(Lambda(K) V) Related to Regular Spreads of PG(V).”
*Electronic Journal of Linear Algebra*20: 354–366. - APA
- De Bruyn, B. (2010). Some subspaces of the projective space PG(Lambda(K) V) related to regular spreads of PG(V).
*ELECTRONIC JOURNAL OF LINEAR ALGEBRA*,*20*, 354–366. - Vancouver
- 1.De Bruyn B. Some subspaces of the projective space PG(Lambda(K) V) related to regular spreads of PG(V). ELECTRONIC JOURNAL OF LINEAR ALGEBRA. 2010;20:354–66.
- MLA
- De Bruyn, Bart. “Some Subspaces of the Projective Space PG(Lambda(K) V) Related to Regular Spreads of PG(V).”
*ELECTRONIC JOURNAL OF LINEAR ALGEBRA*20 (2010): 354–366. Print.