Lower bounds for Betti numbers of monomial ideals

被引：5
|
作者：
Boocher, Adam [1 ]
Seiner, James [2 ]
机构：
[1] Univ Utah, Salt Lake City, UT 84112 USA
[2] Univ Michigan, Ann Arbor, MI 48109 USA
来源：
JOURNAL OF ALGEBRA | 2018年 / 508卷
基金：
美国国家科学基金会;
关键词：
Commutative algebra; Betti numbers; Monomial ideals; Buchsbaum-Eisenbud-Horrocks rank; conjecture; FREE RESOLUTIONS; FINITE-LENGTH; MODULES;
D O I：
10.1016/j.jalgebra.2018.04.013
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let I be a monomial ideal of height c in a polynomial ring S over a field k. If I is not generated by a regular sequence, then we show that the sum of the betti numbers of S/I is at least 2(c) + 2(c-1) and characterize when equality holds. Lower bounds for the individual betti numbers are given as well. (C) 2018 Elsevier Inc. All rights reserved.
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页码：445 / 460
页数：16
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