[Kelly's theorem](https://link.springer.com/article/10.1007%2FBF02187687) states:


Every finite point set of complex space such that the line joining any two points from this set contains at least one more point from this set (every Sylvester-Gallai configaration) is confined to the plane.


The proof is rather short, however it used rather deep result (Bogomolov–Miyaoka–Yau inequality, more accurately, its [corollary](https://link.springer.com/chapter/10.1007%2F978-1-4757-9286-7_7) of F. Hirzebruch).


Are there more simpler proof of Kelly's theorem?


UPD: I have found: <https://arxiv.org/abs/1211.0330>


Also <https://arxiv.org/pdf/math/0403023.pdf> (thank to Mike Miller).



Kelly's theorem about a resolution of the Sylvester–Gallai problem
I have found: <https://arxiv.org/abs/1211.0330>


Also <https://arxiv.org/pdf/math/0403023.pdf> (thank to Mike Miller).


