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On sets defining few ordinary planes
dc.contributor.author | Ball, Simeon Michael |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2017-12-04T11:27:17Z |
dc.date.available | 2018-12-01T01:31:09Z |
dc.date.issued | 2017-09-19 |
dc.identifier.citation | Ball, S. On sets defining few ordinary planes. "Discrete and computational geometry", 19 Setembre 2017, vol. 60, nº 1, p. 1-34. |
dc.identifier.issn | 0179-5376 |
dc.identifier.uri | http://hdl.handle.net/2117/111528 |
dc.description.abstract | Let S be a set of n points in real three-dimensional space, no three collinear and not all co-planar. We prove that if the number of planes incident with exactly three points of S is less than (Formula presented.) for some (Formula presented.) then, for n sufficiently large, all but at most O(K) points of S are contained in the intersection of two quadrics. Furthermore, we prove that there is a constant c such that if the number of planes incident with exactly three points of S is less than (Formula presented.) then, for n sufficiently large, S is either a regular prism, a regular anti-prism, a regular prism with a point removed or a regular anti-prism with a point removed. As a corollary to the main result, we deduce the following theorem. Let S be a set of n points in the real plane. If the number of circles incident with exactly three points of S is less than (Formula presented.) for some (Formula presented.) then, for n sufficiently large, all but at most O(K) points of S are contained in a curve of degree at most four. |
dc.format.extent | 34 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica |
dc.subject.lcsh | Geometry, Algebraic. |
dc.subject.other | Eight associated points theorem |
dc.subject.other | Green–Tao |
dc.subject.other | Ordinary planes |
dc.subject.other | Sylvester–Gallai |
dc.title | On sets defining few ordinary planes |
dc.type | Article |
dc.subject.lemac | Geometria |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.identifier.doi | 10.1007/s00454-017-9935-2 |
dc.subject.ams | Classificació AMS::51 Geometry::51M Real and complex geometry |
dc.relation.publisherversion | https://link.springer.com/article/10.1007%2Fs00454-017-9935-2 |
dc.rights.access | Open Access |
local.identifier.drac | 21556761 |
dc.description.version | Postprint (updated version) |
dc.relation.projectid | info:eu-repo/grantAgreement/MINECO//MTM2014-54745-P/ES/ESTRUCTURAS DISCRETAS, GEOMETRICAS Y ALEATORIAS/ |
local.citation.author | Ball, S. |
local.citation.publicationName | Discrete and computational geometry |
local.citation.volume | Vol 60, n.1 |
local.citation.number | 1 |
local.citation.startingPage | 1 |
local.citation.endingPage | 34 |
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