Rees algebras with minimal multiplicity

Abstract

Let (R,m) be a local ring. Let SM denote the Rees algebra S=R[mrt] localized at its unique maximal homogeneous ideal M=(m,mrt). Let TN denote the extended Rees algebra T= R[mrt, t-1] localized at its unique maximal homogeneous idea N= (t−1,m,mr). Multiplicity formulas are developedfor SM and TN. These are used to find necessaIy and sufficient conditions on a Cohen-Macaulay local ring (R,m) and r so that SM and TN are Cohen-Macaulay with minimal multiplicity