2003/05/31 by Csaba D. Tóth, Csaba D. Toth · 2 citations
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Mathematics and Applications #Point processes and geometric inequalities #math.CO #msc:05B25 #msc:11T99
paper · pdf · doi:10.1007/s00493-014-2686-2
published as Combinatorica 35 (1) (2015), 95-126 · 24 pages, 5 figures, to appear in Combinatorica
arxiv created 2014/05/16 · crossref issued 2015/02/01 · crossref published 2015/02/01 · crossref published-print 2015/02/01 · openalex publication_date 2015/02/01 · crossref created 2015/04/29 · crossref published-online 2015/04/30 · arxiv updated 2015/07/10 · openalex created_date 2016/06/24 · crossref deposited 2019/05/29 · crossref indexed 2026/07/29 · openalex updated_date 2026/07/30
It is shown that n points and e lines in the complex Euclidean plane \mathbb C2 determine O(n2/3e2/3+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 R2.