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

Let I be an -primary ideal in a Cohen–Macaulay local ring of d = dim A ≥ 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 -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.