The multiplicity and the Cohen–Macaulayness of extended Rees algebras of equimultiple ideals

Abstract

Let I be an equimultiple ideal of Noetherian local ring A. This paper gives some multiplicity formulas of the extended Rees algebras T = A[I t, t −1 ]. In the case A generalized Cohen-Macaulay, we determine when T is Cohen-Macaulay and as an immediate consequence we obtain e.g., some criteria for the Cohen-Macaulayness of Rees algebra R(I ) over a Cohen-Macaulay ring in terms of reduction numbers and ideals.