Incidences of not-too-degenerate hyperplanes
György Elekes, Csaba D. Tóth · 2005
We present a multi-dimensional generalization of the Szemerédi-Trotter Theorem, and give a sharp bound on the number of incidences of points and not-too-degenerate hyperplanes in three- or higher-dimensional Euclidean spaces. We call a hyperplane not-too-degenerate if at most a constant portion of its incident points lie in a lower dimensional affine subspace.