Rees algebras with minimal multiplicity

摘要

Let (R,m) be a local ring. Let SMdenote the Rees algebra S=Rmrt localized at its unique maximal homogeneous ideal M=(m,mrt). Let TN denote the extended Rees algebra T= Rmrt, t-1 localized at its unique maximal homogeneous idea N= (t#x2212;1,m,mr). Multiplicity formulas are developedfor SMand TN. These are used to find necessaIy and sufficient conditions on a Cohen-Macaulay local ring (R,m) and r so that SMand TNare Cohen-Macaulay with minimal multiplicity