Polynomial partitioning on varieties and point-hypersurface incidences in four dimensions
Saugata Basu, Martı́n Sombra · arXiv (Cornell University) · 2014
Abstract. We present a polynomial partitioning theorem for finite sets of points in the real locus of a complex algebraic variety. This result generalizes the polynomial partitioning theorem on the Euclidean space of Guth and Katz, and its extension to hypersurfaces by Zahl and by Kaplan, Matouˇsek, Sharir and Safernová. We also present a bound for the number of incidences between points and hypersurfaces in the four-dimensional Euclidean space. It is an application of our partitioning theorem together with the refined bounds for the number of connected components of a semi-algebraic set by Barone and Basu. Contents