The cleanness of (symbolic) powers of Stanley-Reisner ideals

Title:

The cleanness of (symbolic) powers of Stanley-Reisner ideals

Creator:

Bandari, Somayeh and Jahan, Ali Soleyman

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:b1d3c260-ef25-4014-9e87-a6266988bab5
uuid:b1d3c260-ef25-4014-9e87-a6266988bab5
issn:0011-4642

Subject:

complete intersection, matroid, symbolic power, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

Let $\Delta$ be a pure simplicial complex on the vertex set $[n]=\{1,\ldots,n\}$ and $I_\Delta$ its Stanley-Reisner ideal in the polynomial ring $S=K[x_1,\ldots,x_n]$. We show that $\Delta$ is a matroid (complete intersection) if and only if $S/I_\Delta^{(m)}$ ($S/I_\Delta^m$) is clean for all $m\in\mathbb{N}$ and this is equivalent to saying that $S/I_\Delta^{(m)}$ ($S/I_\Delta^m$, respectively) is Cohen-Macaulay for all $m\in\mathbb{N}$. By this result, we show that there exists a monomial ideal $I$ with (pretty) cleanness property while $S/I^m$ or $S/I^{(m)}$ is not (pretty) clean for all integer $m\geq3$. If $\dim(\Delta)=1$, we also prove that $S/I_\Delta^{(2)}$ ($S/I_\Delta^2$) is clean if and only if $S/I_\Delta^{(2)}$ ($S/I_\Delta^2$, respectively) is Cohen-Macaulay., Somayeh Bandari, Ali Soleyman Jahan., and Obsahuje bibliografické odkazy

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

767-778

Source:

Czechoslovak Mathematical Journal | 2017 Volume:67 | Number:3

Harvested from:

CDK

Metadata only:

false