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

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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.

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Acknowledgements

The authors would like to thank the referee for his/her careful reading of the paper and for some suggestions that helped to improve the exposition of this paper.

Funding

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).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11155-9415, Tehran, Iran

    M.R. Pournaki & M. Poursoltani

  2. Department of Mathematics, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama, 700-8530, Japan

    N. Terai

  3. School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran

    S. Yassemi

Authors
  1. M.R. Pournaki
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  2. M. Poursoltani
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  3. N. Terai
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  4. S. Yassemi
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Correspondence to M.R. Pournaki.

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Dedicated with gratitude to our colleague and friend Nguyen Tu Cuong on the occasion of his 70th birthday

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Pournaki, M., Poursoltani, M., Terai, N. et al. A Brief Survey on Pure Cohen–Macaulayness in a Fixed Codimension. Acta Math Vietnam 47, 181–196 (2022). https://doi.org/10.1007/s40306-021-00441-2

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  • DOI: https://doi.org/10.1007/s40306-021-00441-2

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