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arXiv · 1410.8871

Polynomial partitioning for a set of varieties

Larry Guth
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Abstract

Given a set $Γ$ 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 $O(D^{k-n} |Γ|)$ varieties of $Γ$.

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Larry Guth. 2015-07-02. Polynomial partitioning for a set of varieties. https://doi.org/10.1017/s0305004115000468

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