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math.CO2020
A Sylvester-Gallai theorem for cubic curves
Alex Cohen, Frank de Zeeuw
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 is not contained in…
math.CO2020
A Sylvester-Gallai result for concurrent lines in the complex plane
Alex Cohen
We show that if a set of points in lies on a family of concurrent lines, and if one of those lines contains more than points, then there is a line passing…