Some characterizations of Gorenstein Rees Algebras

The aim of this paper is to elucidate the relationship between the Gorenstein Rees algebra (I): =₈ ₀Iⁱ of an ideal I in a complete Noetherian local ring A and the graded canonical module of the extended Rees algebra ' (I): =₈Iⁱ. It is known that the Gorensteinness of (I) is closely related to the property of the graded canonical module of the associated graded ring (I): =₈ ₀Iⁱ/I^i+1. However, there appears to be a shortage of satisfactory references analyzing the relationship between (I) and ' (I) unless the ring (I) is Cohen-Macaulay. This paper provides a characterization of the Gorenstein property of (I) using the graded canonical module of ' (I) without assuming that the base ring A is Cohen-Macaulay. Applying our criterion, we demonstrate that a certain Kawasaki's arithmetic Cohen-Macaulayfication becomes a Gorenstein ring when A is a quasi-Gorenstein local ring with finite local cohomology.