匹配场理想功率的最小细胞分辨率

IF 0.8 2区 数学 Q2 MATHEMATICS
Oliver Clarke , Fatemeh Mohammadi
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引用次数: 0

摘要

我们研究了一类单项式理想,称为块对角匹配场理想,它们是行列式理想的单项式Gröbner退化。我们的重点是这些理想及其所有力量的最低限度的自由解决方案。首先,我们建立了它们的线性商性质,并计算了它们的Betti数,说明了它们的最小自由分辨率在正则CW复合体上是支持的。我们的证明依赖于Herzog和Takayama的结果,证明了具有线性商性质的理想具有最小自由分辨率,以及Dochtermann和Mohammadi对这些分辨率的元胞实现的构造。我们首先证明这种理想的每一个幂的线性商性质。随后,我们证明了它们对应的分解映射是规则的,从而产生最小的细胞分辨率。最后,我们证明了不同的分解图导致不同的细胞复合体具有相同的面数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Minimal cellular resolutions of powers of matching field ideals
We study a family of monomial ideals, called block diagonal matching field ideals, which arise as monomial Gröbner degenerations of determinantal ideals. Our focus is on the minimal free resolutions of these ideals and all of their powers. Initially, we establish their linear quotient property and compute their Betti numbers, illustrating that their minimal free resolution is supported on a regular CW complex. Our proof relies on the results of Herzog and Takayama, demonstrating that ideals with a linear quotient property have a minimal free resolution, and on the construction by Dochtermann and Mohammadi of cellular realizations of these resolutions. We begin by proving the linear quotient property for each power of such an ideal. Subsequently, we show that their corresponding decomposition map is regular, resulting in a minimal cellular resolution. Finally, we demonstrate that distinct decomposition maps lead to different cellular complexes with the same face numbers.
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来源期刊
CiteScore
1.70
自引率
12.50%
发文量
225
审稿时长
17 days
期刊介绍: The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.
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