On (q2 + q + 1)-sets of class [1, m, n]2 in PG(3, q)
A characterization of cones in P G (3, q ) as sets of points of P G (3, q ) of size q 2 + q + 1 projecting from a point V a set of q + 1 points of a plane of P G (3, q ) and with three intersection numbers with respect to the planes is given.
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| Published in | Journal of geometry Vol. 105; no. 3; pp. 449 - 455 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Basel
Springer Basel
01.12.2014
|
| Subjects | |
| Online Access | Get full text |
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| Abstract | A characterization of cones in P
G
(3,
q
) as sets of points of P
G
(3,
q
) of size
q
2
+
q
+ 1 projecting from a point
V
a set of
q
+ 1 points of a plane of P
G
(3,
q
) and with three intersection numbers with respect to the planes is given. |
|---|---|
| AbstractList | A characterization of cones in P
G
(3,
q
) as sets of points of P
G
(3,
q
) of size
q
2
+
q
+ 1 projecting from a point
V
a set of
q
+ 1 points of a plane of P
G
(3,
q
) and with three intersection numbers with respect to the planes is given. |
| Author | Napolitano, Vito |
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| Cites_doi | 10.1007/BF01922493 10.4171/RLM/635 10.4153/CJM-1955-045-x 10.1007/BF00147522 10.36045/bbms/1292334065 |
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| Keywords | quadric cone 51E26 Projective space intersection number |
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| References | De Winter, Schillewaert (CR2) 2010; 17 Segre (CR6) 1955; 7 Panella (CR5) 1955; 10 Thas (CR7) 1973; 1 Barlotti (CR1) 1955; 10 Napolitano, Olanda (CR4) 2012; 23 Korchmaros (CR3) 1980; 15 G. Panella (213_CR5) 1955; 10 A. Barlotti (213_CR1) 1955; 10 B. Segre (213_CR6) 1955; 7 J.A. Thas (213_CR7) 1973; 1 G. Korchmaros (213_CR3) 1980; 15 V. Napolitano (213_CR4) 2012; 23 S. De Winter (213_CR2) 2010; 17 |
| References_xml | – volume: 17 start-page: 911 year: 2010 end-page: 918 ident: CR2 article-title: A note on quasi-Hermitian varieties and singular quasi–quadrics publication-title: Bull. Belg. Math. Soc. Simon Stevin – volume: 15 start-page: 170 issue: 2 year: 1980 end-page: 174 ident: CR3 article-title: On -sets of type (0,1, ) in projective planes publication-title: J. Geom. doi: 10.1007/BF01922493 – volume: 10 start-page: 507 year: 1955 end-page: 513 ident: CR5 article-title: Caratterizzazione delle quadriche di uno spazio (tridimensionale) lineare sopra un corpo finito publication-title: Boll. Unione Mat. Ital. III. Ser. – volume: 23 start-page: 395 year: 2012 end-page: 403 ident: CR4 article-title: Sets of type (3, ) in P (3, ) publication-title: Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl. doi: 10.4171/RLM/635 – volume: 7 start-page: 414 year: 1955 end-page: 416 ident: CR6 article-title: Ovals in a finite projective plane publication-title: Can. J. Math. doi: 10.4153/CJM-1955-045-x – volume: 10 start-page: 498 issue: 3 year: 1955 end-page: 506 ident: CR1 article-title: Un’estensione del teorema di Segre-Kustaanheimo publication-title: Boll. U.M.I. – volume: 1 start-page: 236 issue: 2 year: 1973 end-page: 240 ident: CR7 article-title: A combinatorial problem publication-title: Geom. Dedicata doi: 10.1007/BF00147522 – volume: 7 start-page: 414 year: 1955 ident: 213_CR6 publication-title: Can. J. Math. doi: 10.4153/CJM-1955-045-x – volume: 15 start-page: 170 issue: 2 year: 1980 ident: 213_CR3 publication-title: J. Geom. doi: 10.1007/BF01922493 – volume: 1 start-page: 236 issue: 2 year: 1973 ident: 213_CR7 publication-title: Geom. Dedicata – volume: 10 start-page: 498 issue: 3 year: 1955 ident: 213_CR1 publication-title: Boll. U.M.I. – volume: 10 start-page: 507 year: 1955 ident: 213_CR5 publication-title: Boll. Unione Mat. Ital. III. Ser. – volume: 17 start-page: 911 year: 2010 ident: 213_CR2 publication-title: Bull. Belg. Math. Soc. Simon Stevin doi: 10.36045/bbms/1292334065 – volume: 23 start-page: 395 year: 2012 ident: 213_CR4 publication-title: Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl. doi: 10.4171/RLM/635 |
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| Snippet | A characterization of cones in P
G
(3,
q
) as sets of points of P
G
(3,
q
) of size
q
2
+
q
+ 1 projecting from a point
V
a set of
q
+ 1 points of a plane of P... |
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| StartPage | 449 |
| SubjectTerms | Geometry Mathematics Mathematics and Statistics |
| Title | On (q2 + q + 1)-sets of class [1, m, n]2 in PG(3, q) |
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