Symbolic powers, Serre conditions and Cohen-Macaulay Rees algebras
Let \(R\) be a local Cohen-Macaulay ring and \(I\) an unmixed ideal of \(R\) which is generically a complete intersection and satisfies \(I^{(n)} = I^n\) for all \(n \geq 1\). This paper investigates when the Rees algebras \({\mathfrak R} = R[It]\) and the associated graded ring \(G = \text{gr}_I (R)\) are also Cohen-Macaulay. Several partial answers to these two questions are given in terms of when \(G\) satisfies the Serre condition \((S_r)\).
Cohen-Macaulay property of associated graded ring
scientific article; zbMATH DE number 724679
scientific article