Polynomial partitioning for a set of varieties
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.
Gespeichert in:
| Veröffentlicht in: | Mathematical proceedings of the Cambridge Philosophical Society 2015-11, Vol.159 (3), p.459-469 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | 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. |
|---|---|
| ISSN: | 0305-0041 1469-8064 |
| DOI: | 10.1017/S0305004115000468 |