A Brief Survey on Pure Cohen–Macaulayness in a Fixed Codimension

M. R. Pournaki; M. Poursoltani; N. Terai; S. Yassemi

doi:10.1007/s40306-021-00441-2

A Brief Survey on Pure Cohen–Macaulayness in a Fixed Codimension

M. R. Pournaki, M. Poursoltani, N. Terai, S. Yassemi

School of Science

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

Abstract

A concept of Cohen–Macaulay in codimension t is defined and characterized for arbitrary finitely generated modules and coherent sheaves by Miller, Novik, and Swartz in 2011. Soon after, Haghighi, Yassemi, and Zaare-Nahandi defined and studied CM_t simplicial complexes, which is the pure version of the abovementioned concept and naturally generalizes both Cohen–Macaulay and Buchsbaum properties. The purpose of this paper is to survey briefly recent results of CM_t simplicial complexes.

Original language	English
Journal	Acta Mathematica Vietnamica
DOIs	https://doi.org/10.1007/s40306-021-00441-2
Publication status	Accepted/In press - 2021

Keywords

Buchsbaum ring
Buchsbaum simplicial complex
CM simplicial complex
Cohen–Macaulay ring
Cohen–Macaulay simplicial complex
Simplicial complex

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s40306-021-00441-2

Cite this

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title = "A Brief Survey on Pure Cohen–Macaulayness in a Fixed Codimension",

abstract = "A concept of Cohen–Macaulay in codimension t is defined and characterized for arbitrary finitely generated modules and coherent sheaves by Miller, Novik, and Swartz in 2011. Soon after, Haghighi, Yassemi, and Zaare-Nahandi defined and studied CMt simplicial complexes, which is the pure version of the abovementioned concept and naturally generalizes both Cohen–Macaulay and Buchsbaum properties. The purpose of this paper is to survey briefly recent results of CMt simplicial complexes.",

keywords = "Buchsbaum ring, Buchsbaum simplicial complex, CM simplicial complex, Cohen–Macaulay ring, Cohen–Macaulay simplicial complex, Simplicial complex",

author = "Pournaki, {M. R.} and M. Poursoltani and N. Terai and S. Yassemi",

note = "Funding Information: The research of M.R. Pournaki was in part supported by a grant from The World Academy of Sciences (TWAS–UNESCO Associateship – Ref. 3240295905). The research of N. Terai was in part supported by a grant from The Japan Society for the Promotion of Science (JSPS Grant-in-Aid for Scientific Research (C) – Ref. 18K03244). Publisher Copyright: {\textcopyright} 2021, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.",

year = "2021",

doi = "10.1007/s40306-021-00441-2",

language = "English",

journal = "Acta Mathematica Vietnamica",

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AU - Pournaki, M. R.

AU - Poursoltani, M.

AU - Terai, N.

AU - Yassemi, S.

N1 - Funding Information: The research of M.R. Pournaki was in part supported by a grant from The World Academy of Sciences (TWAS–UNESCO Associateship – Ref. 3240295905). The research of N. Terai was in part supported by a grant from The Japan Society for the Promotion of Science (JSPS Grant-in-Aid for Scientific Research (C) – Ref. 18K03244). Publisher Copyright: © 2021, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.

PY - 2021

Y1 - 2021

N2 - A concept of Cohen–Macaulay in codimension t is defined and characterized for arbitrary finitely generated modules and coherent sheaves by Miller, Novik, and Swartz in 2011. Soon after, Haghighi, Yassemi, and Zaare-Nahandi defined and studied CMt simplicial complexes, which is the pure version of the abovementioned concept and naturally generalizes both Cohen–Macaulay and Buchsbaum properties. The purpose of this paper is to survey briefly recent results of CMt simplicial complexes.

AB - A concept of Cohen–Macaulay in codimension t is defined and characterized for arbitrary finitely generated modules and coherent sheaves by Miller, Novik, and Swartz in 2011. Soon after, Haghighi, Yassemi, and Zaare-Nahandi defined and studied CMt simplicial complexes, which is the pure version of the abovementioned concept and naturally generalizes both Cohen–Macaulay and Buchsbaum properties. The purpose of this paper is to survey briefly recent results of CMt simplicial complexes.

KW - Buchsbaum ring

KW - Buchsbaum simplicial complex

KW - CM simplicial complex

KW - Cohen–Macaulay ring

KW - Cohen–Macaulay simplicial complex

KW - Simplicial complex

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JO - Acta Mathematica Vietnamica

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A Brief Survey on Pure Cohen–Macaulayness in a Fixed Codimension

Abstract

Keywords

ASJC Scopus subject areas

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