一个丰富多彩的hochster公式和通用参数的面环

IF 0.3 4区数学 Q4 MATHEMATICS

Journal of Commutative Algebra Pub Date : 2020-07-25 DOI:10.1216/jca.2023.15.151

Ashleigh Adams, V. Reiner

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引用次数: 2

摘要

本文由两个相关部分组成。第一部分将关于Stanley-Reisner环分辨率的Hochster公式推广到彩色版本，适用于任何简单复合体的适当顶点着色。第二部分考察了简单配合物的Stanley-Reisner环的普遍参数系统，更一般地说，是简单偏置集的面环。这些参数具有在对称条件下的固定性和检测面环深度的良好性能。此外，当在这些参数上解析面环时，形状可以通过彩色Hochster公式进行预测。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A COLORFUL HOCHSTER FORMULA AND UNIVERSAL PARAMETERS FOR FACE RINGS

This paper has two related parts. The first generalizes Hochster's formula on resolutions of Stanley-Reisner rings to a colorful version, applicable to any proper vertex-coloring of a simplicial complex. The second part examines a universal system of parameters for Stanley-Reisner rings of simplicial complexes, and more generally, face rings of simplicial posets. These parameters have good properties, including being fixed under symmetries, and detecting depth of the face ring. Moreover, when resolving the face ring over these parameters, the shape is predicted, conjecturally, by the colorful Hochster formula.

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来源期刊

Journal of Commutative Algebra MATHEMATICS-

CiteScore

0.80

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Commutative Algebra publishes significant results in the area of commutative algebra and closely related fields including algebraic number theory, algebraic geometry, representation theory, semigroups and monoids. The journal also publishes substantial expository/survey papers as well as conference proceedings. Any person interested in editing such a proceeding should contact one of the managing editors.