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On the Number of Ordinary Lines Determined by Sets in Complex Space Basit, Abdul Dvir, Zeev Saraf, Shubhangi Wolf, Charles Incidences Combinatorial Geometry Designs Polynomial Method Kelly's theorem states that a set of n points affinely spanning C^3 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Abdul Basit and Zeev Dvir and Shubhangi Saraf and Charles Wolf 2017 Is Part Of LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2017.15 urn:nbn:de:0030-drops-71883 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.15 eng https://creativecommons.org/licenses/by/3.0/legalcode