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Tubes in PG ( 3 , q )
A tube (resp. an oval tube) in PG ( 3 , q ) is a pair T = { L , L } , where { L } ∪ L is a collection of mutually disjoint lines of PG ( 3 , q ) such that for each plane π of PG ( 3 , q ) containing L , the intersection of π with the lines of L is a hyperoval (resp. an oval). The line L is called t...
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| Published in: | European journal of combinatorics 2006, Vol.27 (1), p.114-124 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Citations: | Items that this one cites |
| Online Access: | Get full text |
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| Summary: | A tube (resp. an oval tube) in
PG
(
3
,
q
)
is a pair
T
=
{
L
,
L
}
, where
{
L
}
∪
L
is a collection of mutually disjoint lines of
PG
(
3
,
q
)
such that for each plane
π
of
PG
(
3
,
q
)
containing
L
, the intersection of
π
with the lines of
L
is a hyperoval (resp. an oval). The line
L
is called the axis of
T
. We show that every tube for
q
even and every oval tube for
q
odd can be naturally embedded into a regular spread and hence admits a group of automorphisms which fixes every element of
T
and acts regularly on each of them. For
q
odd we obtain a classification of oval tubes up to projective equivalence. Furthermore, we characterize the reguli in
PG
(
3
,
q
)
,
q
odd, as oval tubes which admit more than one axis. |
|---|---|
| ISSN: | 0195-6698 1095-9971 |
| DOI: | 10.1016/j.ejc.2004.07.001 |