The Szemerédi-Trotter theorem in the complex plane
- 136 Downloads
It is shown that n points and e lines in the complex Euclidean plane ℂ2 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 ℝ2.
Mathematics Subject Classication (2000)05D99 52C35
Unable to display preview. Download preview PDF.
- P. Erdős: Problems and results in combinatorial geometry, in: Discrete geometry and convexity (New York, 1982), vol. 440 of Ann. New York Acad. Sci., 1985, 1–11.Google Scholar
- G. H. Golub and C. F. Van Loan: Matrix computations, The Johns Hopkins Univ. Press (2nd ed.), Baltimore, MD, 1989, 584–586.Google Scholar
- R. Narasimhan: Analysis on real and complex manifolds, Elsevier (3rd ed.), Amsterdam, 1985, 66–69.Google Scholar
- Y-C. Wong: Differential geometry of Grassmann manifolds, Proc. Nat. Acad. Sci. U.S.A. 47 (1967), 189–594.Google Scholar