四维余维2与点超曲面关联簇的多项式分割
Polynomial partitioning on varieties of codimension two and point-hypersurface incidences in four dimensions
摘要：
本文对余维至多为2的不可约复代数簇的实轨迹上的有限点集给出了一个多项式分割定理。这一结果推广了Guth和Katz在欧几里得空间上的多项式分割定理，以及Zahl和Kaplan、Matoušek、Sharir和Safernová在超曲面上的推广。我们还给出了四维欧几里得空间中点与超曲面的关联数的一个界。它是我们的分割定理的应用，以及由Barone和Basu的半代数集的连通分量数的精确界。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
