论文标题
五颜六色的Hochster公式和面环的通用参数
A colorful Hochster formula and universal parameters for face rings
论文作者
论文摘要
本文有两个相关的部分。首先将Hochster的公式概括为Stanley-Reisner Rings的分辨率，以彩色版本，适用于任何适当的简单复合物的顶点色。第二部分研究了简单复合物的Stanley-Reisner环的通用参数系统，更一般而言，面对简单posets的环。这些参数具有良好的特性，包括固定在对称性下，并检测面环的深度。此外，当在这些参数上解析面环时，通过五颜六色的Hochster公式可以预测形状。
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.
