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A brief survey on pure cohen–macaulayness in a fixed codimension
, Article Acta Mathematica Vietnamica ; 2021 ; 02514184 (ISSN) ; Poursoltani, M ; Terai, N ; Yassemi, S ; Sharif University of Technology
Springer
2021
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. © 2021, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd
A brief survey on pure cohen–macaulayness in a fixed codimension
, Article Acta Mathematica Vietnamica ; Volume 47, Issue 1 , 2022 , Pages 181-196 ; 02514184 (ISSN) ; Poursoltani, M ; Terai, N ; Yassemi, S ; Sharif University of Technology
Springer
2022
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. © 2021, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd