Illinois Journal of Mathematics

Cohen–Macaulay multigraded modules

C.-Y. Jean Chan, Christine Cumming, and Huy Tài Hà

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Let $S$ be a standard $\mathbb{N}^r$-graded algebra over a local ring $A$, and let $M$ be a finitely generated $\mathbb{Z}^r$-graded module over $S$. We characterize the Cohen–Macaulayness of $M$ in terms of the vanishing of certain sheaf cohomology modules. As a consequence, we apply our result to study the Cohen–Macaulayness of multi-Rees modules. Our work extends previous studies on the Cohen–Macaulayness of multi-Rees algebras.

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Illinois J. Math., Volume 52, Number 4 (2008), 1147-1163.

First available in Project Euclid: 18 November 2009

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Primary: 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13C14: Cohen-Macaulay modules [See also 13H10] 14B15: Local cohomology [See also 13D45, 32C36] 14M05: Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10]


Chan, C.-Y. Jean; Cumming, Christine; Tài Hà, Huy. Cohen–Macaulay multigraded modules. Illinois J. Math. 52 (2008), no. 4, 1147--1163. doi:10.1215/ijm/1258554354.

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