Some characterizations of Gorenstein Rees Algebras

The aim of this paper is to elucidate the relationship between the Gorenstein Rees algebra (I):=i≥ 0Iⁱ of an ideal I in a complete Noetherian local ring A and the graded canonical module of the extended Rees algebra '(I):=i∈Iⁱ. 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):=i≥ 0Iⁱ/Iⁱ⁺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.