Szemer\'edi--Trotter-type theorems in dimension 3

By J. Kollár. 2014

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We estimate the number of incidences in a configuration of $m$ lines and $n$ points in dimension 3. The main term is $mn^{1/3}$ if we work over the real or complex numbers but $mn^{2/5}$ over finite fields. Both of these are optimal, aside from a multiplicative constant that is at most 5.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/de1d70f942254e97314f7676a7ece5e0282b8a3c