An incidence theorem in higher dimensions

Abstract

We prove almost tight bounds on incidences between points and $k$-dimensional varieties of bounded degree in ${\mathbb{R}}^d$. Our main tools are the Polynomial Ham Sandwich Theorem and induction on both the dimension and the number of points.

26 pages, no figures. A gap in the proof of Proposition 4.4 has been repaired

References in corpus (6)

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• Simple Proofs of Classical Theorems in Discrete Geometry via the Guth--Katz Polynomial Partitioning Technique
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Cited by in corpus (3)

• Further improvements to incidence and Beck-type bounds over prime finite fields
• On the Wolff circular maximal function
• Refined bounds on the number of connected components of sign conditions on a variety