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Polynomial partitioning for a set of varieties

Published online by Cambridge University Press:  30 September 2015

LARRY GUTH
LARRY GUTH*
Affiliation:
MIT, Department of Mathematics, Building E18, Room 369, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, U.S.A. e-mail: [email protected]
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 159 , Issue 3 , November 2015 , pp. 459 - 469
Copyright
Copyright © Cambridge Philosophical Society 2015 

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References

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