Polynomial partitioning for a set of varieties

Abstract

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 $\Gamma$.

Locations

• Mathematical Proceedings of the Cambridge Philosophical Society - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View