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 [ It , 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.