Article
| 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 |
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| Category: | math |
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| 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 |
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| Date available: | 2022-04-21T19:00:33Z |
| Last updated: | 2022-09-08 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/150408 |
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