Rees algebras of contracted ideals in two-dimensional regular local rings

Abstract

Let ( R, m) be a two-dimensional regular local ring with infinite residue field. For an m-primary ideal I it is proved that the Rees algebra R[ It] (resp. R[ It, t −1]) is a Cohen-Macaulay ring with minimal multiplicity at its maximal homogeneous ideal ( m, It) (resp. ( t −1, m, It)) if and only if for some minimal reduction ( a, b) of I, ( a, b) I = I 2 and there exists an x ϵ m 2 such that IR[ m x ] ∩ R = 1 .