# Kelly's theorem about a resolution of the Sylvester–Gallai problem

Kelly's theorem 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 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).

• There is this, which might suit you.
– mme
Jul 20 '17 at 15:53