Gorensteinness in Rees algebras of powers of parameter ideals

Abstract

This paper gives a necessary and sufficient condition for Gorensteinness in Rees algebras of the dth power of parameter ideals in certain Noetherian local rings of dimension d≥2. The main result of this paper produces many Gorenstein Rees algebras over non-Cohen-Macaulay local rings. For example, the Rees algebra R(qd)=⊕i≥0qdi is Gorenstein for every parameter ideal q that is a reduction of the maximal ideal in a d-dimensional Buchsbaum local ring of depth 1 and multiplicity 2.