%0 Journal Article
%T Polynomial partitioning for a set of varieties
%A Larry Guth
%J Mathematics
%D 2014
%I arXiv
%R 10.1017/S0305004115000468
%X Given a set $\Gamma$ of low-degree k-dimensional varieties in $\mathbb{R}^n$, we prove that for any $D \ge 1$, there is a non-zero polynomial $P$ of degree at most $D$ so that each component of $\mathbb{R}^n \setminus Z(P)$ intersects $O(D^{k-n} |\Gamma|)$ varieties of $\Gamma$.
%U http://arxiv.org/abs/1410.8871v2