On the number of rich lines in high dimensional real vector spaces
  In this short note we use the polynomial partitioning lemma to strengthen a recent result of Dvir and Gopi about the number of rich lines in high dimensional Euclidean spaces. Our result shows that if there are sufficiently many rich lines incident to a set of points then large fraction of them must be contained in a hyperplane. 
Marton Hablicsek and Zachary Scherr
math.CO