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

摘要

Let I be an m-primary ideal in a Cohen-Macaulay local ring (A, m) of d = dimA greater than or equal to 1. The ideal I is said to have minimal multiplicity if mu(A)(I) = e(I)(A) + d - l(A)(A/). There are given criteria for the Cohen-Macaulayness and Gorensteinness in Pees 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 Proj R(I) and the negativity of invariants a(i)(R(I)). A counterexample to a conjecture of Korb and Nakamura will be given. (C) 2000 Elsevier Science B.V. All rights reserved. [References: 20]