Cohen–Macaulayness and negativity of A-invariants in Rees algebras associated to m-primary ideals of minimal multiplicity

Abstract

Let I be an m-primary ideal in a Cohen–Macaulay local ring (A,m) of d=dimA≥1. The ideal I is said to have minimal multiplicity if μA(I)=eI(A)+d−ℓA(A/I). There are given criteria for the Cohen–Macaulayness and Gorensteinness in Rees algebras R(I) and graded rings G(I) associated to m-primary ideals I of minimal multiplicity. The Cohen–Macaulayness in R(I) is explored in connection with that of ProjR(I) and the negativity of invariants ai(R(I)). A counterexample to a conjecture of Korb and Nakamura will be given.