On the Cohen-Macaulay and Gorenstein properties of multigraded Rees algebras (Q1313516)

The aim of this paper is to investigate the Gorensteinness of the multigraded Rees algebra \(R_ A (I^{k_ 1}, \dots, I^{k_ r}) = A[I^{k_ 1} t_ 1, \dots, I^{k_ r} t_ r]\) \((I\) an ideal in the ring \(A)\); the case of graded Rees algebras was investigated by Trung and Ikeda. The main results says that if \(A\) is a local Cohen Macaulay ring and \(I\) is an equimultiple ideal of height at least 2 then the above multigraded Rees algebra is Gorenstein if and only if the Rees algebra \(R_ A (I^{k_ 1 + \dots k_ r})\) is Gorenstein.