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.
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| Veröffentlicht in: | Mathematical proceedings of the Cambridge Philosophical Society 2015-11, Vol.159 (3), p.459-469 |
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| container_title | Mathematical proceedings of the Cambridge Philosophical Society |
| container_volume | 159 |
| creator | GUTH, LARRY |
| description | 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. |
| doi_str_mv | 10.1017/S0305004115000468 |
| format | Article |
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n
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n
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$\mathbb{R}$
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.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S0305004115000468</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0305-0041 |
| ispartof | Mathematical proceedings of the Cambridge Philosophical Society, 2015-11, Vol.159 (3), p.459-469 |
| issn | 0305-0041 1469-8064 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1770289126 |
| source | Cambridge Journals Online |
| subjects | Geometry Mathematical analysis Partitioning Polynomials |
| title | Polynomial partitioning for a set of varieties |
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