Abstract
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.
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