ON THE MULTIPLICITY OF REES ALGEBRAS OF GOOD FILTRATIONS

Abstract

Let (A, m) be a Noetherian local ring. Let F ={I_n}_n≥0 be a good filtration of ideals in A. Denote by R(F) = ⊕_n≥0 I_ntⁿ the Rees algebra of F. In this paper we investigate the mixed multiplicities of F and the relationship between the multiplicity of R(F) and the mixed multiplicities of F. As an application, we obtain several multiplicity formulas that express the multiplicity of R(F) as a sum of Hilbert-Samuel multiplicities of some quotient rings of A.