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The Szemeredi-Trotter Theorem in the Complex Plane

Csaba D. Toth
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Abstract

It is shown that $n$ points and $e$ lines in the complex Euclidean plane ${\mathbb C}^2$ determine $O(n^{2/3}e^{2/3}+n+e)$ point-line incidences. This bound is the best possible, and it generalizes the celebrated theorem by Szemerédi and Trotter about point-line incidences in the real Euclidean plane ${\mathbb R}^2$.

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Csaba D. Toth. 2014-05-16. The Szemeredi-Trotter Theorem in the Complex Plane. https://doi.org/10.1007/s00493-014-2686-2

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