A resolution of the Sylvester-Gallai problem of J.-P. Serre
The author calls a point set a Sylvester-Gallai configuration (SGC) if every line joining two points of the set contains at least one member of the set. Gallai proved that a SGC in the real plane is confined to a line; this can be generalized to ordered projective or affine spaces. The author shows using results of Hirzebruch that a SGC in complex space is confined to a plane (Theorem). A further statement needed is the following: If a SGC of a pappian affine plane is a subset of 3 concurrent lines but not of one line, then the associated field has nonzero characteristic (Lemma 2).
scientific article; zbMATH DE number 3953686