%0 Journal Article %T A note on rich lines in truly high dimensional sets %A Joshua Zahl %J Mathematics %D 2015 %I arXiv %X We modify an argument of Hablicsek and Scherr to show that if a collection of points in $\mathbb{C}^d$ spans many $r$--rich lines, then many of these lines must lie in a common $(d-1)$--flat. This is closely related to a previous result of Dvir and Gopi. %U http://arxiv.org/abs/1503.01729v1