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Jul 10, 2013 at 2:05 comment added Pham Hung Quy If your question has an affirmative amswer then $R/I^{(n)}$ is Cohen-Macaulay iff $R/I^{(n)}$ is Cohen-Macaulay for all $m, n$, where $I^{(n)}$ denotes the $n$th-symbolic power of $I$. This is not true in general (See arxiv.org/pdf/1003.2152.pdf).
Jul 8, 2013 at 20:10 comment added Andrei Thanks, but what if we add, as I said above, the condition $I \subset J$ ?
Jul 8, 2013 at 20:09 vote accept Andrei
Jul 8, 2013 at 14:50 history answered Pham Hung Quy CC BY-SA 3.0