Polynomial partitioning for a set of varieties

By Larry Guth. Mathematical Proceedings of the Cambridge Philosophical Society, 2014

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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 ⩾ 1, there is a non-zero polynomial P of degree at most D so that each component of $\mathbb{R}$ n \Z(P) intersects O(Dk−n |Γ|) varieties of Γ.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

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