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A NOTE ON RICH LINES IN TRULY HIGH DIMENSIONAL SETS

  • JOSHUA ZAHL (a1)
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.

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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.
References
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[2] Bochnak, J., Coste, M. and Roy., M.-F., Real Algebraic Geometry (Springer, Berlin, 1998).
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[7] Harris, J., Algebraic Geometry: A First Course, Graduate Texts in Mathematics, 133 (Springer, New York, 1995).
[8] Sheffer, A. and Zahl, J., ‘Point-curve incidences in the complex plane’, 2015, preprint arXiv:1502.07003.
[9] Solymosi, J. and Tao, T., ‘An incidence theorem in higher dimensions’, Discrete Comput. Geom. 48(2) (2012), 255280.
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Forum of Mathematics, Sigma
  • ISSN: -
  • EISSN: 2050-5094
  • URL: /core/journals/forum-of-mathematics-sigma
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