2020/10/04 by Cohen, Alex, de Zeeuw, Frank
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2010.01513
We prove a variant of the Sylvester-Gallai theorem for cubics (algebraic curves of degree three): If a finite set of sufficiently many points in ℝ2 is not contained in a cubic, then there is a cubic that contains exactly nine of the points. This resolves the first unknown case of a conjecture of Wiseman and Wilson from 1988, who proved a variant of Sylvester-Gallai for conics and conjectured that similar statements hold for curves of any degree.