The Szemeredi-Trotter Theorem in the Complex Plane

Details The Szemeredi-Trotter Theorem in the Complex Plane The Szemeredi-Trotter Theorem in the Complex Plane

2003-05-20

arxiv.org/abs/math/0305283v4

Mathematics

Combinatorics

23 pages, 5 figures, submitted

Scientific paper

It is shown that $n$ points and $e$ lines in the complex Euclidean plane
$\C^2$ 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 Szemer\'edi and
Trotter about point-line incidences in the real Euclidean plane $\R^2$.

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