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

Bart De Bruyn UGent (2010) 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.
author
organization
year
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
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.