On the Eisenbud-Green-Harris conjecture
On the Eisenbud-Green-Harris conjecture
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关于艾森巴德-格林-哈里斯猜想
DOI：
10.1090/s0002-9939-2014-12216-7
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发表时间：
2012
影响因子：
0.6
通讯作者：
Abed Abedelfatah
中科院分区：
文献类型：
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作者：
Abed Abedelfatah
Eisenbud，绿色和Harris证明了：如果I是k[x_1，.中的齐次理想，x_n]$包含一个正则序列$f_1，.，f_n$的度数$\deg（f_i）=a_i$，其中$2\leq a_1\leq... \leq a_n$，则存在包含$x_1^{a_1}，...的齐次理想$J$，x_n^{a_n}$具有相同的希尔伯特函数。本文证明了当f_i$对所有i$分裂为线性因子时的Eisenbud-Green-Harris猜想。
It has been conjectured by Eisenbud, Green and Harris that if $I$ is a homogeneous ideal in $k[x_1,...,x_n]$ containing a regular sequence $f_1,...,f_n$ of degrees $\deg(f_i)=a_i$, where $2\leq a_1\leq ... \leq a_n$, then there is a homogeneous ideal $J$ containing $x_1^{a_1},...,x_n^{a_n}$ with the same Hilbert function. In this paper we prove the Eisenbud-Green-Harris conjecture when $f_i$ splits into linear factors for all $i$.