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 d-th power of parameter ideals in certain Noetherian local rings of dimension d ≥ 2. The main result implies that, for example, the Rees algebra R(q d ) = ⊕ i≥0 q di is Gorenstein for any parameter ideal q that is a reduction of the maximal ideal in a d-dimensional Buchsbaum local ring of depth 1 and multiplicity 2.