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Incidence theorems for pseudoflats. (English) Zbl 1132.52025

Summary: We prove Pach-Sharir type incidence theorems for a class of curves in \(\mathbb R^{n}\) and surfaces in \(\mathbb R^{3}\), which we call pseudoflats. In particular, our results apply to a wide class of generic irreducible real algebraic sets of bounded degree.

MSC:

52C30 Planar arrangements of lines and pseudolines (aspects of discrete geometry)
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
52A15 Convex sets in \(3\) dimensions (including convex surfaces)
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