A note on rich lines in truly high dimensional sets

Abstract

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.

10 pages, 0 figures. Accepted for publication in FoM, Sigma

References in corpus (2)

• Point-curve incidences in the complex plane
• On the number of rich lines in high dimensional real vector spaces

Cited by in corpus (1)

• Point-curve incidences in the complex plane