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On the number of ordinary lines determined by sets in complex space

Author(s): Basit, A; Dvir, Zeev; Saraf, S; Wolf, C

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dc.contributor.authorBasit, A-
dc.contributor.authorDvir, Zeev-
dc.contributor.authorSaraf, S-
dc.contributor.authorWolf, C-
dc.date.accessioned2018-07-20T15:08:46Z-
dc.date.available2018-07-20T15:08:46Z-
dc.date.issued2017en_US
dc.identifier.citationBasit, A, Dvir, Z, Saraf, S, Wolf, C. (2017). On the number of ordinary lines determined by sets in complex space. 77 (151 - 1515. doi:10.4230/LIPIcs.SoCG.2017.15en_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1pq2d-
dc.description.abstractKelly's theorem states that a set of n points affinely spanning C3 must determine at least one ordinary complex line (a line passing through exactly two of the points). Our main theorem shows that such sets determine at least 3n/2 ordinary lines, unless the configuration has n - 1 points in a plane and one point outside the plane (in which case there are at least n - 1 ordinary lines). In addition, when at most n/2 points are contained in any plane, we prove a theorem giving stronger bounds that take advantage of the existence of lines with four and more points (in the spirit of Melchior's and Hirzebruch's inequalities). Furthermore, when the points span four or more dimensions, with at most n/2 points contained in any three dimensional affine subspace, we show that there must be a quadratic number of ordinary lines.en_US
dc.format.extent151 - 1515en_US
dc.language.isoen_USen_US
dc.relation.ispartof33rd International Symposium on Computational Geometry, SoCG 2017en_US
dc.rightsAuthor's manuscripten_US
dc.titleOn the number of ordinary lines determined by sets in complex spaceen_US
dc.typeConference Articleen_US
dc.identifier.doidoi:10.4230/LIPIcs.SoCG.2017.15-
dc.date.eissued2017en_US
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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