Almost complete intersections and the Lex-Plus-Powers Conjecture
Almost complete intersections and the Lex-Plus-Powers Conjecture
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几乎完全交集和 Lex-Plus-Powers 猜想
DOI：
10.1016/j.jalgebra.2003.09.016
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发表时间：
2004
影响因子：
0.9
通讯作者：
Christopher A. Francisco
中科院分区：
文献类型：
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作者：
Christopher A. Francisco
证明了分次Betti数上的Lex-Plus-Powers猜想的几乎完全相交情形。我们证明了一个lex-plus-powers几乎完全交的分解提供了任何其他理想的分次Betti数的一个上界，这些理想具有相同次数的正则序列和相同的Hilbert函数。一个关键因素是找到两个Koszul复合物之间的显式比较图。最后，我们得到了几乎完全交的Hilbert函数的界，包括Eisenbud-Green-Harris猜想的一个特例。
We prove the almost complete intersection case of the Lex-Plus-Powers Conjecture on graded Betti numbers. We show that the resolution of a lex-plus-powers almost complete intersection provides an upper bound for the graded Betti numbers of any other ideal with regular sequence in the same degrees and the same Hilbert function. A key ingredient is finding an explicit comparison map between two Koszul complexes. Finally, we obtain bounds on the Hilbert function of an almost complete intersection, including a special case of a conjecture of Eisenbud–Green–Harris.