2014/06/09 by Saugata Basu, Martı́n Sombra, Basu, Saugata +2
Computer Science · Mathematics · #14P25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #G.2.1 #Polynomial and algebraic computation #Primary 52C10 #Secondary 13D40 #acm:13D40 #acm:14P25 #acm:52C10 #cs.CG #math.AC #math.AG #math.CO #msc:13D40 #msc:14P25 #msc:52C10
paper · pdf · doi:10.48550/arxiv.1406.2144
23 pages. Some explanations added
openalex publication_date 2014/06/09 · arxiv created 2015/09/20 · arxiv updated 2015/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a polynomial partitioning theorem for finite sets of points in the real locus of an irreducible complex algebraic variety of codimension at most two. 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, Matoušek, 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.