斯坦利-赖斯纳理想与纯粹的决心

arXiv - MATH - Commutative Algebra Pub Date : 2024-09-09 DOI:arxiv-2409.05481

David Carey, Moty Katzman

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引用次数: 0

摘要

我们研究具有纯解析的 Stanley-Reisner 理想。为此，我们引入了 PR 复数族，即其对偶 Stanley-Reisner 理想具有纯解析的简单复数。我们提出了两个高度对称的 PR 复数无限族。我们还证明了斯坦利-瑞斯纳理想的第一个博伊-索"{o}德尔伯格猜想的部分类比，通过详细的分析方法，我们可以构造出除初始移位 $c_0$ 之外的任何给定形状的具有纯贝蒂图的斯坦利-瑞斯纳理想。

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Stanley-Reisner Ideals with Pure Resolutions

We investigate Stanley-Reisner ideals with pure resolutions. To do this, we introduce the family of PR complexes, simplicial complexes whose dual Stanley-Reisner ideals have pure resolutions. We present two infinite families of highly-symmetric PR complexes. We also prove a partial analogue to the first Boij-S\"{o}derberg Conjecture for Stanley-Reisner ideals, by detailing an algorithm for constructing Stanley-Reisner ideals with pure Betti diagrams of any given shape, save for the initial shift $c_0$.

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arXiv - MATH - Commutative Algebra

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