Geodesic
A NOTE ON RICH LINES IN TRULY HIGH DIMENSIONAL SETS
Forum of Mathematics, Sigma, Tome 4 (2016)

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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. 
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     author = {JOSHUA ZAHL},
     title = {A {NOTE} {ON} {RICH} {LINES} {IN} {TRULY} {HIGH} {DIMENSIONAL} {SETS}},
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JOSHUA ZAHL. A NOTE ON RICH LINES IN TRULY HIGH DIMENSIONAL SETS. Forum of Mathematics, Sigma, Tome 4 (2016). doi: 10.1017/fms.2015.34

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