Arithmetical rank of squarefree monomial ideals of small arithmetic degree

Kyouko Kimura; Naoki Terai; Ken Ichi Yoshida

doi:10.1007/s10801-008-0142-3

Arithmetical rank of squarefree monomial ideals of small arithmetic degree

Kyouko Kimura, Naoki Terai, Ken Ichi Yoshida

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

22 Citations (Scopus)

Abstract

In this paper, we prove that the arithmetical rank of a squarefree monomial ideal I is equal to the projective dimension of R/I in the following cases: (a) I is an almost complete intersection; (b) arithdeg∈I=reg∈I; (c) arithdeg∈I=indeg∈I+1. We also classify all almost complete intersection squarefree monomial ideals in terms of hypergraphs, and use this classification in the proof in case (c).

Original language	English
Pages (from-to)	389-404
Number of pages	16
Journal	Journal of Algebraic Combinatorics
Volume	29
Issue number	3
DOIs	https://doi.org/10.1007/s10801-008-0142-3
Publication status	Published - May 2009
Externally published	Yes

Keywords

Alexander duality
Almost complete intersection
Arithmetic degree
Arithmetical rank
Initial degree
Regularity

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

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10.1007/s10801-008-0142-3

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AB - In this paper, we prove that the arithmetical rank of a squarefree monomial ideal I is equal to the projective dimension of R/I in the following cases: (a) I is an almost complete intersection; (b) arithdeg∈I=reg∈I; (c) arithdeg∈I=indeg∈I+1. We also classify all almost complete intersection squarefree monomial ideals in terms of hypergraphs, and use this classification in the proof in case (c).

KW - Alexander duality

KW - Almost complete intersection

KW - Arithmetic degree

KW - Arithmetical rank

KW - Initial degree

KW - Regularity

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Arithmetical rank of squarefree monomial ideals of small arithmetic degree

Abstract

Keywords

ASJC Scopus subject areas

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