Discrete & Computational Geometry

, Volume 48, Issue 2, pp 255–280

An Incidence Theorem in Higher Dimensions


DOI: 10.1007/s00454-012-9420-x

Cite this article as:
Solymosi, J. & Tao, T. Discrete Comput Geom (2012) 48: 255. doi:10.1007/s00454-012-9420-x


We prove almost tight bounds on the number of incidences between points and k-dimensional varieties of bounded degree in Rd. Our main tools are the polynomial ham sandwich theorem and induction on both the dimension and the number of points.


Szemerédi–Trotter type incidence theoremsSum-product bounds

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.UCLA Department of MathematicsLos AngelesUSA