On the Gorensteinness of Rees algebras over local rings

Abstract

Let (A, m, k ) be a Noetherian local ring and I an ideal of A . We set and call this graded A -algebra the Rees algebra of I . The importance of the Rees algebra R(I ) is in the fact that Proj R(I ) is the blowing up of Spec A with center in V(I ). The Cohen-Macaulayness of Rees algebras was studied by many mathematicians. In [GS] S. Goto any Y. Shimoda gave a criterion for R(m ) to be Cohen-Macaulay under the assumption that A is Cohen-Macaulay. Their results have been generalized to R(I ) in [HI].