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Some cases of the Eisenbud-Green-Harris conjecture
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Caviglia, Giulio and Maclagan, Diane (2008) Some cases of the Eisenbud-Green-Harris conjecture. Mathematical Research Letters, Vol.15 (No.3). pp. 427-433. ISSN 1073-2780.
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Abstract
The Eisenbud-Green-Harris conjecture states that a homogeneous ideal in $\K[x_1,\dots,x_n]$ containing a homogeneous regular sequence $f_1,\dots,f_n$ with $\deg(f_i)=a_i$ has the same Hilbert function as an ideal containing $x_i^{a_i}$ for $1 \leq i \leq n$. In this paper we prove the Eisenbud-Green-Harris conjecture when $a_j > \sum_{i=1}^{j-1} (a_i-1)$ for all $j>1$. This result was independently obtained by the two authors.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Mathematical Research Letters | ||||
Publisher: | Mathematical Publishing | ||||
ISSN: | 1073-2780 | ||||
Official Date: | May 2008 | ||||
Dates: |
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Volume: | Vol.15 | ||||
Number: | No.3 | ||||
Page Range: | pp. 427-433 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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