| Title:
|
On the symmetric algebra of certain first syzygy modules (English) |
| Author:
|
Restuccia, Gaetana |
| Author:
|
Tang, Zhongming |
| Author:
|
Utano, Rosanna |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
72 |
| Issue:
|
2 |
| Year:
|
2022 |
| Pages:
|
391-409 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(R,\frak {m})$ be a standard graded $K$-algebra over a field $K$. Then $R$ can be written as $S/I$, where $I\subseteq (x_1,\ldots ,x_n)^2$ is a graded ideal of a polynomial ring $S=K[x_1,\ldots ,x_n]$. Assume that $n\geq 3$ and $I$ is a strongly stable monomial ideal. We study the symmetric algebra ${\rm Sym}_R({\rm Syz}_1(\frak {m}))$ of the first syzygy module ${\rm Syz}_1(\frak {m})$ of $\frak {m}$. When the minimal generators of $I$ are all of degree 2, the dimension of ${\rm Sym}_R({\rm Syz}_1(\frak {m}))$ is calculated and a lower bound for its depth is obtained. Under suitable conditions, this lower bound is reached.\looseness -1 (English) |
| Keyword:
|
symmetric algebra |
| Keyword:
|
syzygy |
| Keyword:
|
dimension |
| Keyword:
|
depth |
| MSC:
|
13C15 |
| MSC:
|
13D02 |
| idZBL:
|
Zbl 07547211 |
| idMR:
|
MR4412766 |
| DOI:
|
10.21136/CMJ.2021.0508-20 |
| . |
| Date available:
|
2022-04-21T19:00:33Z |
| Last updated:
|
2024-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150408 |
| . |
| Reference:
|
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