论文标题
Eisenbud-Green-Harris猜想，用于快速增长的序列
The Eisenbud-Green-Harris conjecture for fast-growing degree sequences
论文作者
论文摘要
让$ s $是一个字段上的标准分级多项式环，而$ i $是一个均质的理想，其中包含常规序列$ d_1，\ ldots，d_n $。当常规序列的形式满足$ d_i \ geqslant \ sum_ {j = 1}^{i-1}（d_j-1）$时，我们证明了Eisenbud-green-harris的猜想，并改善了第一作者在2008年获得的结果。除了Güntürkün和Hochster最近证明的常规序列的零星情况外，本文的结果还恢复了所有已知的猜想案例，其中仅固定了常规序列的程度，并包括几个。
Let $S$ be a standard graded polynomial ring over a field, and $I$ be a homogeneous ideal that contains a regular sequence of degrees $d_1,\ldots,d_n$. We prove the Eisenbud-Green-Harris conjecture when the forms of the regular sequence satisfy $d_i \geqslant \sum_{j=1}^{i-1}(d_j-1)$, improving a result obtained in 2008 by the first author and Maclagan. Except for the sporadic case of a regular sequence of five quadrics, recently proved by Güntürkün and Hochster, the results of this article recover all known cases of the conjecture where only the degrees of the regular sequence are fixed, and include several additional ones.
