A Sylvester-Gallai result for concurrent lines in the complex plane

2020/07/07 by Cohen, Alex · 1 citation
#51A45 #52C30 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.03601

Abstract

We show that if a set of points in ℂ² lies on a family of m concurrent lines, and if one of those lines contains more than m-2 points, then there is a line passing through exactly two points of the set. The bound m-2 in our result is optimal. Our main theorem resolves a conjecture of Frank de Zeeuw, and generalizes a result of Kelly and Nwankpa.

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• Sylvester--Gallai configurations on algebraic curves in C²

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