Multigraded Rees algebras of [formula omitted]-primary ideals in local rings of dimension greater than one

Abstract

Let I 1,…, I g be m -primary ideals in a local ring (R, m) . Set R[ It ]≔R[I 1t 1,…,I gt g] and M=( m,I 1t 1,…,I gt g) . In this paper we show that if R is a Cohen–Macaulay (CM) local ring of dimension greater than two and if R[ It ] M is CM with minimal multiplicity, then g=1.