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A NOTE ON RICH LINES IN TRULY HIGH DIMENSIONAL SETS

Part of: Discrete geometry

Published online by Cambridge University Press:  13 January 2016

JOSHUA ZAHL
JOSHUA ZAHL*
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA, USA; jzahl@mit.edu

Abstract

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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.

MSC classification

Primary: 52C35: Arrangements of points, flats, hyperplanes
Secondary: 52C10: Erdős problems and related topics of discrete geometry
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 4 , 2016 , e2
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author 2016

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