Polynomial partitioning for a set of varieties
Larry Guth · Mathematical Proceedings of the Cambridge Philosophical Society · 2015
Abstract Given a set Γ of low-degree k-dimensional varieties in $\mathbb{R}$ n, we prove that for anyD⩾ 1, there is a non-zero polynomialPof degree at mostDso that each component of $\mathbb{R}$ n\Z(P) intersectsO(Dk−n|Γ|) varieties of Γ.