Sylvester-Gallai Theorems for Complex Numbers and Quaternions by Noam Elkies and others

By Noam Elkies, Lou M. Pretorius and Konrad J. Swanepoel. Discrete & Computational Geometry 35 (2006), 361–373. Author preprint: arxiv.org/abs/math/0403023

Locator: introduction, real Sylvester-Gallai theorem and the extensions to complex and quaternionic projective spaces.