The Szemeredi-Trotter Theorem in the Complex Plane

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 ${\mathbb{R}}^2$.

24 pages, 5 figures, to appear in Combinatorica

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