论文标题
cohen-macaulay simpicial复合物的史丹利 - 赖斯纳戒指上不变的不平等现象
Inequalities of invariants on Stanley-Reisner rings of Cohen-Macaulay simplicial complexes
论文作者
论文摘要
本文的目的是研究Cohen-Macaulay simplicial dimension $ d-1 $的Cohen-Macaulay简单复合物的Stanley-Reisner Rings的一些代数不变。我们证明，不平等$ d \ leq \ mathrm {reg}（δ）\ cdot \ cdot \ cdot \ mathrm {type}（δ）$适用于任何$（d-1）$ - 尺寸cohen-macaulay simpleicial simpleicial complect $δ$Δ$δ$满足$δ= \ m core umm mathrm} $ ne $ ntumeutme ummate um n $ ntume um { （分别$ \ mathrm {type}（δ）$）表示Stanley-Reisner Ring $ \ bbbk [Δ] $的Castelnuovo-Mumford Quaranity（分别cohen-Macaulay type）。此外，对于任何给定的整数$ d，r，t $满足$ r，t \ geq 2 $和$ r \ leq d \ leq d \ leq rt $，我们构建了一个Cohen-Macaulay Simpleicial Complect $δ（G）$作为图$ G $的独立络合物，以$ G $的独立络合物$ \ mathrm {type}（δ（g））= t $。
The goal of the present paper is the study of some algebraic invariants of Stanley-Reisner rings of Cohen-Macaulay simplicial complexes of dimension $d - 1$. We prove that the inequality $d \leq \mathrm{reg}(Δ) \cdot \mathrm{type}(Δ)$ holds for any $(d-1)$-dimensional Cohen-Macaulay simplicial complex $Δ$ satisfying $Δ=\mathrm{core}(Δ)$, where $\mathrm{reg}(Δ)$ (resp. $\mathrm{type}(Δ)$) denotes the Castelnuovo-Mumford regularity (resp. Cohen-Macaulay type) of the Stanley-Reisner ring $\Bbbk[Δ]$. Moreover, for any given integers $d,r,t$ satisfying $r,t \geq 2$ and $r \leq d \leq rt$, we construct a Cohen-Macaulay simplicial complex $Δ(G)$ as an independent complex of a graph $G$ such that $\dim(Δ(G))=d-1$, $\mathrm{reg}(Δ(G))=r$ and $\mathrm{type}(Δ(G))=t$.
