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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: 2024-07-01
Stable URL: http://hdl.handle.net/10338.dmlcz/150408
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