Licci squarefree monomial ideals generated in degree two or with deviation two

Kyouko Kimura; Naoki Terai; Ken ichi Yoshida

doi:10.1016/j.jalgebra.2013.06.001

Licci squarefree monomial ideals generated in degree two or with deviation two

Kyouko Kimura, Naoki Terai, Ken ichi Yoshida

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

We study squarefree monomial ideals which are in the linkage class of a complete intersection (we call such an ideal licci). Firstly we classify all licci edge ideals. Secondly we prove that any Cohen-Macaulay almost complete intersection squarefree monomial ideal is licci. Thirdly we characterize licci squarefree monomial ideals of deviation 2 in terms of hypergraphs associated to the ideals as an application of the classification in Kimura, Terai and Yoshida (2009) [15].

Original language	English
Pages (from-to)	264-289
Number of pages	26
Journal	Journal of Algebra
Volume	390
DOIs	https://doi.org/10.1016/j.jalgebra.2013.06.001
Publication status	Published - Sep 5 2013
Externally published	Yes

Keywords

Cohen-Macaulay ring
Deviation
Edge ideal
Hypergraph
Licci
Linkage
Monomial ideal

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2013.06.001

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title = "Licci squarefree monomial ideals generated in degree two or with deviation two",

abstract = "We study squarefree monomial ideals which are in the linkage class of a complete intersection (we call such an ideal licci). Firstly we classify all licci edge ideals. Secondly we prove that any Cohen-Macaulay almost complete intersection squarefree monomial ideal is licci. Thirdly we characterize licci squarefree monomial ideals of deviation 2 in terms of hypergraphs associated to the ideals as an application of the classification in Kimura, Terai and Yoshida (2009) [15].",

keywords = "Cohen-Macaulay ring, Deviation, Edge ideal, Hypergraph, Licci, Linkage, Monomial ideal",

author = "Kyouko Kimura and Naoki Terai and Yoshida, {Ken ichi}",

note = "Funding Information: This work was partially supported by JSPS Grant-in-Aid for Scientific Research (C) 22540047/23540053 , JSPS Grant-in-Aid for Young Scientists (B) 24740008 .",

year = "2013",

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doi = "10.1016/j.jalgebra.2013.06.001",

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T1 - Licci squarefree monomial ideals generated in degree two or with deviation two

AU - Kimura, Kyouko

AU - Terai, Naoki

AU - Yoshida, Ken ichi

N1 - Funding Information: This work was partially supported by JSPS Grant-in-Aid for Scientific Research (C) 22540047/23540053 , JSPS Grant-in-Aid for Young Scientists (B) 24740008 .

PY - 2013/9/5

Y1 - 2013/9/5

N2 - We study squarefree monomial ideals which are in the linkage class of a complete intersection (we call such an ideal licci). Firstly we classify all licci edge ideals. Secondly we prove that any Cohen-Macaulay almost complete intersection squarefree monomial ideal is licci. Thirdly we characterize licci squarefree monomial ideals of deviation 2 in terms of hypergraphs associated to the ideals as an application of the classification in Kimura, Terai and Yoshida (2009) [15].

AB - We study squarefree monomial ideals which are in the linkage class of a complete intersection (we call such an ideal licci). Firstly we classify all licci edge ideals. Secondly we prove that any Cohen-Macaulay almost complete intersection squarefree monomial ideal is licci. Thirdly we characterize licci squarefree monomial ideals of deviation 2 in terms of hypergraphs associated to the ideals as an application of the classification in Kimura, Terai and Yoshida (2009) [15].

KW - Cohen-Macaulay ring

KW - Deviation

KW - Edge ideal

KW - Hypergraph

KW - Licci

KW - Linkage

KW - Monomial ideal

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